Science topic

# Finite Difference - Science topic

Explore the latest questions and answers in Finite Difference, and find Finite Difference experts.

Questions related to Finite Difference

How can anyone measure reflection coefficient from the PML region, using FDTD, in a hollow (εr=1) rectangular wave guide, knowing only the fields for every time step inside the wave guide, while the fields inside PML are not extracted? Is there a straightforward way?

i want Finite Volume Method in easy way, which can easily solve the Elliptic and Parabolic Equations involving measure data, please suggest the relevant books or links which can solve it easily.

The inhomogeneous heat equation is described as follows:

Ut - kUxx = f(x,t). In order to solve this inhomogeneous PDE, Are there any restrictions on the type of the function f(x,t)? Even / Odd or neither?

Thanks

Kulthoum

Background: I am an ok coder but have not learned to use either of the above programs, both of which are freely available to me at my workplace and both of which I have been told will basically do the job with general numerical methods.

Extra background: The models I'm working with are black holes, so they are singular at at least one boundary (the event horizon), meaning that an adaptive step size method must be used; and given that there are essentially more free parameters to a general solution at infinity than at the event horizon, we sometimes need to use a "shooting" technique where we take 'initial' conditions at (near) both boundaries and try to match them up in the middle.

I can work out/look up the numerical recipes for the methods - but any advice on which programming language is more suitable would be greatly appreciated. Also, show your working ;)

Hi,

anyone knows anything about calculating shear stress near a wall in an orthogonal helical coordinate system? I want to calculate it using finite difference but I don't know how to start.

Hello,

what does splitting finite difference scheme mean and how is it different from the regular finite difference methods??

Thanks in advance :)

- Is there any way to increase memory usage to generate 50x50x50 m of mesh size 0.1 m. first it does not run. and hang for hours and then it takes 12 hours for 1 step?

Hello,

i am new at this area and want to simulate an one dimensional spherical transient cooling with convective boundary condition. I am using the finite difference explicit method.

My question is, how can i concert the time step from the finite difference explicit method to the fourier number / dimensionless number? My time step is delta_t = t_Max / (t_Nodes - 1)

The equation for Fourier number is Fo = alpha*t/L. Is the t every time step in my simulation? Where is the definition that my timestep has the unit seconds?

I need the dimensionless time to validate my results.

My conductive heat equation is:

rho * c * dT/dt = k * (d2T/dr2 + 2/r * dT/dr)

After approximation (explicit method):

rho * c * (T(n+1,m) - T(n,m)/delta_t = k * {[T(n,m-1) - 2T(n,m) + T(n,m+1)]/delta_r^2 + 2/[(m-1)*delta_r] * [T(n,m+1) - T(n,m-1)]/(2*delta_r)}

The equation for the temperature at next step is:

T(n+1,m) = (k*delta_t)/(rho*c*delta_r^2)*{T(n,m-1) - 2T(n,m) + T(n,m+1) + (T(n,m+1) - T(n,m-1))/(m-1)} + T(n,m)

One boundary condition on the sphere surface is:

rho*c*dT/dt = k*dT/dr + h*(T∞ - T(n,m))

-> T(n+1,m) = (delta_t)/(rho*c) * {k*(T(n,m+1) - T(n,m)/delta_r + h*(T∞ - T(n,m))} + T(n,m)

Am i on the right way to solve the problem with spherical cooling with transient heat transfer with convective boundary condition on one site?

Thx for help!

d2y/dx2 =y2/(2+x) ; y(0)=1, y(2)=1.

for the above equation ,

1) how to apply the shooting method

2) how to write the matlab code

3) how to get the numerical results

Thanks in advance

Am I correct in saying that a hyper-finite frequentist account of probability would require not just absolute convergence of relative frequencies in the absolute limit but an absolute arithmetic convergence of the actual frequencies (so if the events are equally probable there must only be equal relative frequencies but precisely the same number of each event!;

So that necessarily on even odds, an agent will break precisely if the probability or relative frequencies are precisely 0.5; I say this because I would presume that even only tiny difference say finite difference between the number of A events in ~A events in an infinite collective would disturb the relative frequency if takes into account infinetismals.

It would make 0.5 + infinitesimal and if frequentist require necessary convergence to the probability values, and the probability values is precisely 0.5, then convergence has in some sense failed.

Would this strong kind of convergence have implications on place selection rules and the kinds of dependency that occur between events (events would appears to be more inter-connected, or teleological in a hyperfinite account as it cannot even account for the minutest of differences).

Likewise I presume the laws of large numbers (outside of frequentism would have to be different) ; i presume that even if one says that convergence only occurs with probability 1-infinismal, if infinitesimals infect the frequencies as well I presume that probability of gettting precisely that relative frequency is infinitesimal not 1- infinitesimal and so that infinesimals would have to placed around both the relative frequencies and probabilities values ie

Pr(lim>inf{ relative frequency of A in [Pr(A)-infinesimal, Pr(A) + infinesimal] }=1- infinitesimal; otherwise they would have to say that convernce is almost surely not going to occur, and if they do the above the difference between measure theoretical or more kolmogorovian nonstandard models and nonstandard frequentist models becomes much greater

I am going to solve Richards equation for unsaturated zone using finite difference method. I read in several papers that van Genuchten method is used to estimate hydraulic properties. In van Genuchten formula we can estimate theta and K. what is the difference between the theta obtained by van Genuchten formula and the theta obtained by Richards equation. The other question is that in solving Richards equation we assume an initial h. in the next step h should be estimated so that we can calculate using this equation. How it can be updated in each step.

If there is any what is the difference or similarity ?

Hello,

Anyone could explain the physical meaning of the partial differential equation coefficients in the propagation of elastic waves in solid media?

Equations for isotropic solid media in 2D:

Equation 1: ρ (∂ ^ 2 u_x) / (∂t ^ 2) = (2G + λ) (∂ ^ 2 u_x) / (∂x ^ 2) + G (∂ ^ 2 u_x) / (∂y ^ 2) + (G + λ) (∂ ^ 2 u_y) / ∂x∂y

Equation 2: ρ (∂ ^ 2 u_y) / (∂t ^ 2) = G (∂ ^ 2 u_y) / (∂x ^ 2) + (2G + λ) (∂ ^ 2 u_y) / (∂y ^ 2) + (G + λ) (∂ ^ 2 u_x) / ∂x∂y

Recalling that I understand what the physical parameters (G; λ) themselves represent for the specific physical problem, but I do not know what is the physical implication of its use as a multiplier of each partial derivative.

Thanks in advance for the help.

Renato

How do you implement a higher order finite difference schemes, like 5th or 7th order scheme, or a 6th order central scheme near boundaries? As in, near boundaries you don't have enough points to implement such schemes. What do you do in such cases?

Note that the boundary conditions are not periodic. There will be inflow, outflow and wall boundary conditions.

Thank you in advance:)

Since the nonlinear term can be discretized nonlocally in several ways, what properties do you need to look at to make the best choice?

I consulted several works but could not get any suitable reasoning for the reason of reattachment of the bubble downstream of the flow except the fact that the separated bubble reattaches in the fluid at a point, known as

*Saddle point*. I am in search of physics of reattachment.I am trying to discretize steady Navier Stokes equations for flat plate boundary layer. But I am facing problems in convergence of the iterative solution.

I realize compact finite difference schemes and lattice Boltzmann methods are popular techniques for CAA.

On the other hand, there are very few articles on CAA using finite volume techniques.

Are there particular reasons why CAA using finite volume techniques are not popular?

I am performing frequency calculations for an adsorbate on a small surface with tested parameter setups. But the calculation always stops without error notices. The last message was "Harmonic frequencies will be computed by finite diferences", "Number of displacement per atom is: 2", "Step size for finite difference is： 0.01 Bohrs".

It seems the caclulation stops for no reason.

My system is composed of 40 atoms, not a large system.

I will be very appreciated if you can help.

All the best

Haiping

how the equation formula propagation of microwave heating on the material, using the method of finite different time domain? thank you..

please I want some references about the finite difference schemes for the convective terms in the navier stokes equation .

thanks my friends .

I am interested in determining sump depth for DCC of cylindrical billets when the solidus and liquidus temperatures of the aluminum alloy are known.

So I want to plot temperature v/s cast length(z) along the center line(r=0) i.e. solving heat conduction in cylindrical coordinates

Can I use MATLAB for this?

The problem i'm working on is a boundary layer problem where the resultant equation is a coupled partial differential equation.The equations are linearised and finite difference has been substituted which ends up as a system of equation which can be written as AX=B.where A is a block tridiagonal matrix.

It's known that we can approximate a solution of parabolic equations by replacing the equations with a finite difference equation. Namely, we can solve parabolic equations by Difference Equation Replacement or Crank-Nicolson methods. I need Matlab code of Crank-Nicolson method for attached problem

Is there any alternative explicit method instead?

Dear all Do you know if there's any alternative explicit methods for the treatement of the material nonlinearity, instead of the incremental iterative classical methods? The children in the class shall have to know

Sincerly..

Classical numerical methods (Finite difference, Finite volume, Finite Element,... rely on a mesh to solve the problem. The Finite Element Method (FEM)and Finite Volume Method (FVM) may be the most well-known members of these thoroughly developed mesh-based methods. In contrast, a comparably new class of numerical methods has been developed which approximates partial differential equations only based on a set of nodes without mesh.

Hi,

The stability condition for 1-D heat transfer equation is a*delta_t/delta_x^2 <0.5 in finite difference method.

Is it also valid if i use explicit finite element method?

Thanks

*I have the following problem:*

*u_t = u_xx + u_yy, in Omega, t > 0*

*u(x,y,0) = 1, in Omega*

*u(x,y,t) = 0, on dOmega, t > 0*

*when Omega is defined to be a domain between the rectangular 1x1 and the circle of radius 0.3 centered at (0.5,0.5). dOmega denotes the boundary of the domain Omega.*

I want to solve the problem

**numerically using explicit scheme**for dx = dy = 1/50. And I want to solve it in MATLAB.So far i got a general scheme for all the points, the problematic and non-problematic ones. But I don't know how to compute it.

I want some code that can, for each point, detect the value of alpha and beta (the coefficients in front of dx, dy when the distance to a neighboring grid point is less than dx or dy, i.e. when the neighboring grid point is on the boundary of the circle), for every point on the grid.

Can anyone help me figure out how to compute this?

Any material or suggestion about the above said problem?

In the finite element program known to me, the failure criterion is defined in the p'-q diagram. Is there a program that defines the break criterion in Sigma 1, Sigma 2, Sigma 3 space?
The problem is that with overconsolidated clays the horizontal in situ stresses are overestimated, if the soil model is only defined by p'-q space.

Can anyone help me for Matlab codes for CFD, CRN , CRP which are various methods for sensitivity analysis?

Hello , I am new to numerical methods and I have come across 2 system of non linear PDE that describes flow through a fractured porous media. I have used finite difference to discretize the sets of equation but I cannot really go on from there. FDM is the only method I know but would appreciate other ways of solving it if its something I can follow. Can anyone help me find the best way to solve these equations ? please find attached system of equations.

The wave equation in one space dimension can be written as follows:

∂2u/∂t2 =a ∂2u/∂x2+ b ∂2u/∂y2

This equation is typically described as having only one or two space dimension "x", and "y" because the only other independent variable is the time "t". The question is what is the stability criteria when using the explicit finite difference method?

I need to solve the Fokker-Planck equation numerically. I need to know which method is the best method for solving this kind of PDE? among Finite difference, Finite element, Finite volume, Spectral methods, or any other kinds of methods?which ones is the best choice? and by the "best Method" I mean stable and fast numerical method.

COMSOL v5.1 has possibility to use an Adaptive method to define Curvilinear coordinates system. According to description of the method, the adaptive method adapts the computed vector field to maintain a constant streamline density on the cross section.

1) What is mathematical or physical background of the Adaptive method?

2) What are system of equations and boundary conditions used to compute vector field in Adaptive method?

Thank you in advance,

Algis

Dear all,

I want to know that what is the reason of the usage of FEM in fluid mechanics. Isn't FVM better than FEM?

Why some softwares like COMSOL sill use FEM?

Is FEM has any advantages over FVM?

Which is better?

Regards,

Some times tetrahedral mesh is better and some times hexahedral mesh elements are approximate the material in better way. I want to know the conditions. Advantages and disadvantages of these type of solid 3D elements.

Hi, I have a question the possibility of importing results from a FDTD simulation (3D) into COMSOL and solve a combined heat transfer/fluid dynamics problem. I want to compare the results I get through a complicated Finite difference volume technique with (I presume), faster to obtain, results from COMSOL

I need to solve the cable equation unidimensional using finite differences.

The solution of Schrodinger equations in cylindrical coordinates are written in the form of Bessel functions, by applying the boundary conditions, one has to deal with (Adding, Dividing or Multiplying) for Bessel functions in order to get the allowed energy values

Hello,

I am currently working on the k.p method, and more specifically the application of this method, for the calculation of electronic bands in quantum well structure.

I would like to use finite difference method for my calculation on matlab software, unfortunately I am a newbie in this technique. I think I can generate the code to create the discretized hamiltonian but I don't know how to resolve it and treat the eigenvalues.

Does anyone have a detail algorithm, or some article related to the problem ?

What type of code are you using? Is it Finite difference or Finite element method? Is that a Matlab code related to Gerya 2010?

when we calculate the scattered field with PML and non- PML boundary condition for chiral media

I am trying simulate an infinite domain so I need to use non-reflective boundary conditions. While searching, I came across PML method, but I have certain doubts.

1) How to decide the dimensions of the PML layer?

2) What effect does PML mesh size have on the reflected waves?

I am using TNO DIANA and I simulated a block of soil of 50 m subjected to an impulse load and tried to see the wave travel. I used PML lengths of 10 to 50 m . However, I can still see waves reflecting back. I also tried to increase the function values assigned at the PML boundaries, but after one point I see that the PML behaves like a clamped or fixed boundary. Can someone point me to a source where PML is explained clearly?

Thank you very much.

Hi

I am coding a D2Q9 incompressible flow, and i wanted to try MRT.

After some reading, i saw i need to choose some parameters.

How should i Find those parameters?

Thanks In Advance

Hello beautiful minds

I have to analyse a simple microwave structure using the Boundary Integral-Resonant Mode Expansion (BI-RME) where I have to calculate the coefficients Aij, Bij, Cij and Kp in order to calculate the admittance matrix. Well, for Aij and Bij it's a simple formula, however, for Cij and Kp I should solve Helmholtz's equation in a 2D domain (Laplacian (U (x, y)) + Kp ^ 2 U (x, y) = 0), so after several attempts, I can find neither Cij nor Kp. I was wondering if someone might be able to give me a help by answering my questions below:

1- the analytical formula of eigenfunction U(x,y) depends on two natural constants (m,n)?

2- How many eigenvalues I should take in consideration to get best results?

I'll appreciate if you add some detail exemplification.

thanks for any help you can provide.

So far, I have tried RK method of order 4 and looking for something better.

For example: While solving a 3-phase fluid flow equation, can we use the finite difference for the mathematical model and finite volume for the physical model.

I am solving a parabolic PDE with compact finite difference schemes and I don't have the exact solution for that. So how can I obtain the spatial order of convergence and temporal order of convergence separately for the above PDE because double mesh principle gives the global order of convergence (to the best of my knowledge).

the doubt is " how to apply the boundary condition in timenshenko beam using finte difference technique "?

If any one able to send the sample code for timoshenko beam , to my mail id

I have programmed 2D magnetotelluric forward modeling using both finite difference and finite element method . i want efficiency analysis of these pregame. What is the best way to do this ?

I am trying to write a finite difference code in Matlab to solve the Kirchhoff's plate equation. So far, I have been able to generate the biharmonic/bilaplacian operator matrix. However, I am struggling with how to impose the boundary condition. I would be glad is someone can help explain how to achieve this.

I have taken the liberty of attaching here an m.file I found on the net prepared by

I. Danaila, P. Joly, S. M. Kaber & M. Postel. The task is to use this to generate the biharmonic operator matrix of the kirchhoff's plate equation (which I also have taken the liberty to attach here as well). Thanks

I read recently that "it is not possible to get second order accuracy at the boundaries using finite difference method, were as same is possible with finite volume method. Which by the way is one of the differences between finite difference and finite volume method." Can anyone give me a better insight into this?

Thanks!

Can we approximate the solution to a singular IVP on a domain that extends past a known singularity?

As an example, consider the problem

y' = y^2, y(0) = c > 1,

on the interval [0,1]. The solution is given by

y(x) = c / (1 - cx), x in [0,1] and x =/= 1/c,

and has a singularity at 1/c. Is there a finite method that approximates the solution on [0,1] and handles the singularity in a reasonable way?

Caution: complete ignorance on display in 3...2...1..

I know that econometrics doesn't use "fixed effect" and "random effect" in the way that biostatistics does. I've got the dim idea that both are actually "random effects" in the sense that I would use them, except the econometrics "fixed effect" is correlated with the predictors, and the approach to solving involves taking finite differences. However, I'm trying to find a more concrete description, preferably from someone out there who may have worked with both.

This is primarily driven by my own desire to understand these tools better than I do, but I'm also aware there may be a reason to poach -- er, adapt -- tools from other disciplines. I'm also concerned that one day I may be talking to an economist or social scientist and, as someone once said about the US and the UK, we'd find ourselves separated by a common tongue.

Thanks!

It is accepted that given a 2nd order linear or nonlinear ODE au'' + bu' + cu where a, b,c can be functions of x,u,u' with the prime denoting derivative wrt x and that if initial values are prescribed then the solution can be obtained using Runge-Kutta methods etc while if boundary values are prescribed then the ODE could be solved using the Finite Element or Finite difference Method. My question is why can't an Initial value Problem (IVP) be solvable using the Finite Element method?

My question is limited to ODE's and PDE's are excluded. Basically I am asking why can't an IVP involving an ODE of 2nd order and above be solvable by FEM. Note that the heat-type PDE u

_{t}= c*u_{xx}can be solved via FEM because the problem is of 1st order wrt time derivative and 2nd order wrt spatial derivative. This PDE usually presents an IVP in time but a BVP with x.FEM or finite difference ? Thanks all, Si

I have doubt in Analysis the mode shape and natural frequency of timoshenko beam in matlab using finite difference technique

clear all;close all;clc;

% FD T-beam program for nonuniform,cross section of beams.

a=0; %initial position of fish in "x axis "

b=1; % final position of fish in "x axis "

N=60; % number of cycle

M=4; %for the first 12 value

alpha=0.25; % CONSTANT

R=4500; % R = Slenderness ratio

E=200e9;

I=0.0001171;

A=0.0097389;

p=76.5e3; %desnsity

%2. main calcultion

x=linspace(a,b,N);

h=x(2)-x(1);

hs=h*h;

ht=2*h;

I1=eye(N,N);

I1(1,1)=0;

I1(N,N)=0;

for j=2:N-1

D1(j,j-1)=-1;

D1(j,j+1)=1;

D2(j,j-1)=1;

D2(j,j)=-2;

D2(j,j+1)=1;

end

By1=[1,zeros(1,N-1)];

Bf1=[1,zeros(1,N-1)];

ByN=[zeros(1,N-4),-1,4,-5,2];

BfN=[zeros(1,N-4),-1,4,-5,2];

ma=[alpha*D2,alpha*D1;...

alpha*R*D1,D2-alpha*R*I1];

[Vv,Ev]= eig(ma);

for m=1:6

k=0;

for j=1:2:N

jj=j+N;

k=k+1;

Wv(k,m)=Vv(j,m);

Uv(k,m)=Vv(jj,m);

y(k)=x(j);

end

end

plot(y,Wv(:,2),y,Uv(:,2),'*')

%xlabel('Modes 2 Y=solid, F=dashed','x','Y (amplitude) and F (shear)')

%xgrid

I have doubt in Analysis the mode shape and natural frequency of timoshenko beam in matlab using finite difference technique ,

the doubt is " how to apply the boundary condition in timenshenko beam using finte difference technique "?

If any one able to send the sample code for timoshenko beam , to my mail id

Hello, I am writing a code to resolve an advection problem in 2D, I am using finite elements with a mesh in which there are many triangles. And all my nodes are numbered so I which to know if there is some one who can help me by providing me some ideas/articles where i can find a solution for the calcul of my nodes gradients in x diection and y direction. For example for rectangular mesh, expression of gradients are like this u_x(i) = (u(i+1)-u(i-1))/2dx . Thank you for any information that could help.

who can provide a code for the 2D space fractioanl equation by the finite difference schemes?

Which dimensionless numbers should be taken into account in the stability analysis of a numerical method for Unsteady Convection-Diffusion Problems?

I'm trying to develop a 3D Cylindrical FDTD code with CPML boundary conditions regarding a simulation of a waveguide. So, CPML will be located at the far end of the waveguide along the z-axis (propagation axis). The Z coordinate should be stretched also and pml conductivity should be scaled according to a numeric profile. Usual FDTD equations include the term (2epsilon-sigma*dt)/(2epsilon+sigma*dt) regarding conductivity inside the medium. But CPML equations also use the term conductivity to describe the scaled quantity used in them. With only z stretching, only rho and phi components' PML equations use the scaled conductivity (in this case z-component of coductivity via the convolution terms). The question is, should I use the z-component of the scaled conductivity in the update equations of Ez component, or it should be used ONLY for the stretched components' equations (namely Erho and Ephi in this case)?

To approximate numerically the solution U we consider the Galerkin space discretization and time discretizations based on the Crank-Nicolson method and on the fourth-order Padé approximation R2,2.

What are the steps required to compute the approximate solution Un+1 at the time level tn+1 using both these discretization schemes?

Which one shows more stability and accuracy of the numerical solutions?

1). Lax-Wendroff method with consistent mass matrix

2). Lax-Wendroff method with diagonal mass matrix

How can we introduce dynamic effects in FLAC3D itasca codes?

In the famous book of A. Taflove "Computational Electrodynamics" magnetic field time updates are about n+3/2 and n+1/2 timesteps. The same time updates in Numerical Electromagnetics - the FDTD Method - U. Inan, R. Marshall (Cambridge, 2011) appeared between n+1/2 and n-1/2 timesteps. I know that there is no difference between them, as there is only one timestep between two different times, but I think that I am missing something. Any help will be appreciated.

If any one knows how implement the PML absorbing boundary condition in full acoustic wave equation using finites differences of second order in time and space. I want to compare with the conditions implemented by Cerjan (which multiply the preasure in an exponential factor), I think PML are formulated in a different manner not as a factor.

In the case of my research, I'm using direct numerical simulation to compute the flow around a cylinder for the laminar case (Reynolds around ~ 100) using high order finite difference scheme (6th order). The cylinder is subjected to one-degree-of-freedom vortex-induced vibration in the transverse direction to the flow (y axis).

Right now, I compute the aerodynamic/hydrodynamic coefficients (drag and lift coefficient) using the conservation of momentum equation which uses a control volume. Due to the cylinder displacement, there is a lot of noise in the time signal of the coefficients.

Is this the most efficient way that minimizes numerical error? For example, a paper by Shiels (2001) uses a vorticity formulation to compute aerodynamic coefficients (referred on link).

I want to calculate

**order of accuracy**of Finite Difference Scheme with**non-uniform grids**. Here**analytical solution**is not available. Please suggest some idea..While reading an articles on Shock capturing schemes for high speed flow, i encounter the jargon "dissipative term" several times. Can you please explain me what does it mean particularly? Which term in governing equations represent it? It will also be helpful if you can suggest some literature to be familiar with the jargon used in CFD?

numerical model of dehumidifier has been solved using the finite difference scheme.

I am trying to solve time dependent Ginsburg Landau equations for superconductor-vortex structure using Finite Difference Method (forward time centered space). Set of equations and time development are shown in the attached file.

I am trying to solve the same set of equations using the above said scheme in FORTRAN.

1. my results are not as same as reported in this paper.

2. vortexes in my calculation are not dynamic (they appear at specific positions but do not move rather new vortexes appear at new positions)

3. in my calculation vortexes appear at very low magnetic field setting (i.e. h=0.82 but these figures are at h=10)

solution develops from boundary to inside in FDM, is it the reason that i cannot get correct picture at an intermediate time step? I have been working for several months on this equation and i am stagnant at this point.

Any Suggestion would be extremely encouraging for me..

Dear Friends,

i tried to model tunnel supports using beam elements in FLAC 2D. now i have a problem with calculating the SF of Beams in the model

Thanks in advance

Can we use interchangeably the convolution operator and the finite difference one?

In the some 2D image application cases, one can confuse these two operators, The steady state of an iterated convolution leads to same results as the one of the finite difference operator. can some one give some proofs to this proposition.

Hello, I am developing a simple 3D fortran solver in finite difference using Modified SMAC scheme. My domain is 2pi*2pi*1 as taken by S. Chandrasekhar. My equations are having non dimensional parameters as Reynolds Number, Rayleigh Number and Prandtl No.

The code is running well but w- velocity contours(heating at bottom and cold at top) are coming only positive and negative alternatively and i am not getting rolls as expected. Can someone explain it.? Thanks in advance

Edge detection, w-mask , finite difference, image processing

Hello, I tried to determine the dynamic coefficients of a 2 groove journal bearing, the program is attached, I tried to compare the results obtained by other researchers such as SOMEYA & LUND but the results show a significant difference.

I would be thankful if anyone review the program, or if there an existed one that I can use.

thanks in advance.

Hi, Folks!

I am going to use finite displacement (sometimes called finite difference if I am right) to calculate phonon of my crystal. As I read from some articles and online forums, we should build a supercell first, then move one atom each atom by a given distance. I have two questions concerning supercell.

1)How could I know how large supercell (2*2*2 or 3*3*3 or even larger) I need to build to satisfy the phonon calculation?

2)What's more, should I also increase k-points correspondingly? For example, if I use 4*3*3 for unit cell, then I need to increase to 32*24*24 in case of 2*2*2 supercell.

Hi,

I know integrating u and v will give me the streamfunction at each point in a grid but can someone explain me how to achieve this using finite difference numerical integration in MATLAB ?

Hello, I have a nonlinear PDE with complex numbers(i.e. imaginary) with three variables two of them was calculated by another equation using FDM, now I want to solve this eq. but I don't know how to use FDM with the complex term.

The equation is attached.

Any help.

Anybody can explain why WENO scheme is not considered to be TVD.

Is there any implication of this fact on reconstruction data having large gradients ?

What about MPWENO, is this method abstain the emergence of oscillation in the vicinity of large gradients when using WENO?

How to include the flux boundary over irregular aquifer domain using finite difference analysis??

Can anyone gives me the details description of two level finite difference approximation method?

Dear all,

I'm trying to model the breakthrough curve for an adsorption packed bed column. By making use of a Crank-Nicolson scheme I've discretized the general mass balance equation (diffusion advection equation) where I now want to add a source term which will describe the actual adsorption.

I'm building the model according to the following article since the same assumptions are valid for my model:

I did not succed in modeling the adsorption term in the model. I'm unsure how I have to discretize this term in the axial direction. I was advised to add the adsorption term by making use of the fractional step method. Is there anyone who has experience with this?

All forms of help are highly appreciated!

Cheers,

Stijn

Hello everybody,

I have implemented a numerical model which consists--among others--of a Finite Difference scheme that is used to solve the quasi-stationary magnetic diffusion equation in three dimensions; i.e., a modified version of the Laplacian operator in Cartesian coordinates. For solving the generated system of linear equations (A)x = b I use the SOR algorithm. The model ran well so far, no matter what input I chose. I should mention that the system matrix A consists of complex-valued elements.

However, for some input parameters the SOR solver does not deliver useful results, or more specifically, it does not converge to the given level of accuracy at all. The system matrix has 8e6x8e6 entries which shouldn't be a problem because, for most input parameters, the SOR algorithm delivers physically correct results. It has to have something to do with the entries of the system matrix per se.

For solving the equation on the Cartesian grid I use the 7-point-stencil. If the unmodified version of the Laplacian operator is solved, the weighing factor at the actual node (i,j,k) is -6. In my modified version, it is -6 + i*x, where x denotes the imaginary part. I even tried SPQR from the SuiteSparse package provided by Tim Davis but since this is not an iterative method MATLAB throws an "out of memory" error (I can use up to 192 GiB (!)). It would really be great if someone encountered a similar problem and wants to share their solution. If interested, I could upload the system matrix as well as the boundary condition vector.

Thank you very much in anticipation!

Best regards,

Chris Volkmar

I was working on a simulation of Heat transfer block process that contain (liquid, steam and superheated steam). Unfortunately, all the equations of the heat transfer model consist of a 3rd order P.D.E., I already know the finite element, finite volume and finite difference method. However, applying those methodology never worked with my situation here

So, I wonder if their is a more simpler way for numerical solving of P.D.E. I am currently using MATLAB r2010a to run the simulations

Thanks in advance for any contribution to this subject

Best Regards,

In FLAC geosynthetic is model as linear elastic material. Is it possible to simulate failure of geosynthetic due to large deformation? I am using FLAC

^{3D}version 3.1.There are many functions whose anti-derivatives (primitives), even though they exist, cannot be expressed in terms of elementary functions (like exponential functions, logarithms, trigonometric functions, inverse trigonometric functions and their combinations). I want to ask if it was the same for anti-difference operator of some functions. In other words , can we express the anti-difference operator exponential functions "exp(P(x))" in terms of elementary functions?

I am trying to write the matlab code for following expression :

u(i-(1/2),j+1)+u(i+(1/2),j+1)+u(i+(3/2),j+1)=u(i-(1/2),j)+u(i+(1/2),j)+u(i+(3/2),j) , i=1 to n-2, j=1 to m, with initial condition and Dirichlet conditions.

Dear all.

i would understand more the difference between finite elements analysis and finite difference analysis (eg; plaxis vs Flac)?

best regards.

Dear all

can i know how to apply the inclined load with the software FLAC 2D?

Why is the phase of the input wavelet rotated +- 45º when 2D finite difference modeling is performed for seismic wave propagation?

By Dablain (1986) and others I know that this does not happen for 1D and 3D modeling, only for 2D. Could someone provide me also some reference?

Hi,

I am trying to use Chebyshev pseudospectral method to simulate 3D wave propagation problems. The solver works but is very unstable. I applied mapping functions to make the boundary mesh grid larger but still instability is very apparent.

I read staggered grid tends is helpful in improving the stability of a finite difference solver. I am wondering if that can applied to pseudospectral method. How can it be used in Chebyshev method, in particular?

Any suggestions will be appreciated. Thanks.

Bo

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