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# Finite Difference Method - Science topic

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

Questions related to Finite Difference Method

Please, can the Newmark-beta method for time integration be used in conjunction with the finite difference method (specifically central difference) for the spatial nodes to accurately solve the beam equation? I am trying to implement this for the 4th-order Euler-Bernoulli beam equation with fixed boundary conditions.

How to access/read the state variable (m_epdev) from inside the Fish UDM in FLAC for various grid zones, like the central zone (2, 2) and adjacent zones (3, 2), (1, 2), (2, 3), and (2, 1), at each iteration step?

(1,3) (2,3) (3,3)

(1,2) (2,2) (3,2)

(1,1) (2,1) (3,1)

**Required: state variable (m_epdev) value at each zone at each iteration step inside Fish UDM.**

A fruitful reply will be highly appreciated.

Regards,

Dipaloke

I am trying to mathematically model the derivative of the Dirac delta function for the Euler-Bernoulli beam equation using the finite difference method. I have tried using the Gauss and Lorentz delta sequence kernel, but neither could model the Dirac delta accurately for the piezo-beam equation. Any advice would be appreciated.

If there is 2 DOF (Translational, Rotational) Cantilever beam, and it has 7 elements, I want to use System reduction technique to get rid of the rotational Dof, Do I expect to obtain the same first seven natural frequencies?

Because I tried to use SEREP technique and I did not get the first seven natural frequencies, I got the 1,3,5,7,9,11,13 natural frequencies?

Does anyone has explanations please?

- Two-dimensional Steady State Conduction in a Slab Irradiated by a High Energy Laser Beam at The Surface: Use the finite difference method to solve a two-dimensional steady state conduction in a rectangular aluminum (k =200 W/m C) slab subjected to a constant surface heat flux irradiated by a high-energy laser beam at the top surface. For simplicity, assume the heat flux distribution to be to be a constant average value IO = 2 X 108 W/m2 acting over a section of the surface equal to the beam diameter, d=4mm as shown in the figure. The remaining portion of the top surface is subjected to convection with hc=100W/㎡ C. All other surfaces are assumed to be maintained at constant temperature of 𝑇∞=25 C.

I am analyzing RC beam under elevated temperature using heat transfer approach. The temperature is applied uniformly over the entire surface. I have also defined Amplitude and thermal interaction.

There is no variation in nodal temperature.

Is there any issue in modelling?

#FEM #ABAQUS #heattransfer

Hi

I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.

Can someone please help me with coding a a general expression of n-stencils (where n<m, with m being the number of points) for a second order differential matrix (using finite differences). I have the following code, but it is not giving me the matrices I'm looking for. Thanks in advance.

function D = myfinD()

x = chebpts(6);

%x = linspace(-1,1,6)';

stencils = 3;

x_ = chebpts(stencils);

%x_ = linspace(-1,1,stencils)';

n = numel(x);

d2L = zeros(n,stencils); % Defining an empty matrix

for i = 1:stencils

dL = zeros(n,1);

for k = 1:n

if (x_(i)~=x(k))

for l = 1:n

if (x_(i)~=x(l) && l~=k)

Lprod = ones(n,1);

for j = 1:stencils

if (x_(i)~=x_(j) && j~= k && j~=l)

Lprod = Lprod.*(x-x_(j))/(x_(i)-x_(j));

end

end

dL = dL + Lprod/((x_(i)-x(k))*(x(k)-x(l)));

end

end

end

end

d2L(:,i) = dL;

end

full(d2L)

if (rem(stencils,2)~=0)

if (stencils ~= 1)

m = (stencils-1)/2;

D = spdiags(d2L, -m:m, n, n);

else

D = spdiags(d2L, 0, n, n);

end

full(D)

else

m = stencils/2;

D = spdiags([d2L(:,1:m),zeros(n,1),d2L(:,m+1:end)], -m:m, n, n);

full(D)

end

% confirmation of a three stencil FDS

m = numel(x);

D2 = zeros(m,m);

h = diff(x);

h1 = h(1:end-1); h2 = h(2:end);

d1 = 2./(h1.*(h1+h2)); d2 = -2./(h1.*h2); d3 = 2./(h2.*(h1+h2));

D2(2:end-1,2:end-1) = spdiags([d3 d2 d1], -1:1, m-2, m-2).';

D2(2,1) = d1(1); D2(end-1,end) = d3(end);

full(D2)

I am trying to solve a two dimensional elastic problem of following image to find out stress, strain, displacement of the body under the given condition. I intend to use finite difference method for solving the problem

I tried phonon calculation using the following tag in INCAR for a Double Perovskite material.

IBRION = -1, EDIFF = 1e-8, IALGO = 38, ISMEAR = 0, SIGMA = 0.05, ADDGRID = .TRUE, ENCUT = 350, LREAL = .FALSE, LWAVE = .FALSE, LCHARG = FALSE, PREC = Accurate. NELM = 150

But convergence is not achieved even after a lot of cycles. (attached screenshot)

Kindly suggest...

Various methods are used to solve and analyze fluid flow problems. One of the methods is the Finite difference method. I wanted to know where can we get some general codes of finite difference methods to learn and implement them.

I am trying to solve a time-dependent diffusion equation with finite-difference discretizations using the Newton–Raphson method. However, I encountered some problems in convergence--the solution result changes when changing time step size. Here I want to find some coding examples to refer to. Thank you.

Hi everyone,

I am currently trying to create a contour plot(ABAQUS) of relative micromotions between two surfaces in contact. I have already developed a method for calculation of relative motions. However, I haven't been able to assign my obtained values to the nodes of the geometries that I am evaluating.

Until now, I have read that some people use subroutines to track paired nodes between two surfaces in contact and then they assign the obtained values in a form of a contour plot. Alternatively, developing a MATLAB code and creating a sort of scatter plot with the relative micromotions has also been discussed on some research works.

Nevertheless, I am trying to find a more friendly alternative that doesn't involve a developed code or the use of subroutines.

Creating a field variable from field output is not an option because the first task is to pair closest nodes between surfaces in contact, which is not possible using the operators available here.

If I need to explain myself better, I can provide more details. I will really appreciate any help on this matter.

I'm trying to redo an article (file attached) that uses the

**hybrid finite difference method - the differential transformation method (DTM FDM)**to solve heat conduction problems. I have used Maple but there is something wrong. Can someone help me fix the code?Can anyone please help me write a MATLAB program to find the temperature distribution (By numerical method) across a composite building wall subjected to periodic boundary conditions?

I have the following Laplace's equation on rectangle with length a and width b (picture is attached):

ΔU(x,y)=0

Ux(0,y)=0 : Isolated boundary

Ux(a,y)=f(y) : Current source

U(x,b)=0 : Zero potential

The fourth boundary is quite complex : Mixed boundary condition (isolated except in two points)

if x=a/3 or 2a/3

U(x,0)=0

else

Uy(x,0)=0

Is there an analytical way to solve this kind of mixed boundary problem? can someone point me to the right direction? I'm a bit lost

thanks in advance

Dear all,

What are the factors to be taken into consideration when modeling stone columns in FLAC 3D? Are there differences between the modeling of stone columns and piles?

I am working on lid driven cavity problem in porous media. I have calculated the fluid flow using finite difference method and average nusselt number by simpson rule varying y from 0 to 1. I don't know how to calculate the entropy generation and bejan number which is described in the attached figure.

THANKS

Can someone explain to me the difference between forward difference method and the backward difference method?

Just to discuss on advantages of CFDMs

What are the advantages of Finite volume method (FVM) over Finite difference Method (FDM) for particularly flow simulation (CFD) ?

In Ansys dynamics explicit module, I have modeled a water tank for an earthquake analysis to observe sloshing behavior. I am interested in how Ansys solves the problem using conservation of mass, momentum, and Energy. I have used the eulerian body for water and the lagrangian domain for the water tank. My question Is it using the Finite Element Method (FEM) or Finite Volume Method (FVM) or Finite Difference Method (FDM)? to solve the PDE's

how Silvaco solves the mathematical model. Is it using Finite Element Methods or Finite Difference Methods?

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

Or we have to choose in trial and error method, so the properties of the continuous system are preserved. Basically, I new help in the system of nonlinear odes.

I want to solve a second-order non-linear and non-homogenous order differential equation using the non-linear shooting method and fourth-order Runk Gutta using Python?

Thank you for your help!

Hi, my name is Christopher and I'm currently doing a research in solving the linear elasticity equations using finite difference scheme as a part of my undergraduate thesis. I have been able to solve for the static linear elasticity (displacement formulation) using the finite difference scheme. However, I'm unable to solve the dynamic linear elasticity (velocity-stress formulation) equations using finite difference (Central Time and Central Space FD). The solution always diverges with time.

Here are the first order hyperbolic governing equation i used:

(∂V_x)/∂t=1/ρ ((∂σ_xx)/∂x+(∂σ_xy)/∂y)

(∂V_y)/∂t=1/ρ ((∂σ_yy)/∂y+(∂σ_xy)/∂x)

(∂σ_xx)/∂t=(λ+2μ) (∂V_x)/∂x+λ (∂V_y)/∂y

(∂σ_yy)/∂t=(λ+2μ) (∂V_y)/∂y+λ (∂V_x)/∂x

(∂σ_xy)/∂t=μ((∂V_x)/∂y+(∂V_y)/∂x)

Central Time Central Space FD scheme:

∂f/∂t=(f^(n+1)-f^(n-1))/2∆t

∂f/∂x=(f_(i+1)^n-f_(i-1)^n)/2∆x

The domain i'm trying to simulate is a 2D cantilever beam with fixed displacement on one end and shear stress on the other end. The rest is traction free boundary.

Attached is an apple-to-apple comparison among Spectral Element Method (SEM), Finite Difference Method (FDM) and Finite Element Method (FEM). The accuracy achieved by FEM or FDM with 100 nodes can be achieved by SEM with 10 nodes.

In my opinion, researchers don't consider SEM just because of complexity in coding when compared with FEM or FDM. But when it comes to accuracy, no way.

Note: here I mean the low order FEM

I'm looking for a commercial code that solves fluid mechanics problems via the Finite Difference Method.

hello,

I hope that you are doing well and that the beginning of March is excellent. First of all, I would like to thank the researchers who responded to my last discussion on terrestrial albedo.

Today's discussion is about a problem I found in the numerical modeling of the convection phenomenon (heat transfer)

the goal is to dimension the prototype to be able to dimension it, so I used the finite difference method to discretize the equations of order 1 (I discretized time by a forward scheme and space by a backward scheme).

Despite this and after I wrote a program on python to be able to extract the results, I found values that are not logical for example the water temperature by heating with a radiation value of the order 500 W/m^2 -10 °C.

someone will give me an idea on what I should do or change ... ? the scheme? .........

thank you in advance

cordially

Firyal LATRACHE

Hello everyone, hope all is good.

I want to analyse multi-phase fluid flow through pipe, which software is best to do so ?

During AM process, progressively activation of elements can predict the temperature/crystallinity history, including surroundings heat losses and than this data could be used to determine the deformation as well as the residual stresses within Abaqus AM plugin as one can do from user subroutines like UMATHT -> UMAT ? Are there any differences in term of results or convergence one have analyzed?

Dear Colleagues, I stated a discussion related to this few days before.

Really I am facing the problem .

I want to solve the Radial wave functions for Hydrogen atom for degenerate states like n= 2, 3 ....

For n= 2 , there are two different radial wave functions corresponding to l= 0 and l= 1.

I am using Finite difference method .

I am getting the energy Eigen values but failed to get the degenerate wave functions.

Please help me to get the problem solved.

Thanks and Regards

N Das

May I know is there a way to get the Deff of a slab with 3 terms where n=0,1,2. I have looked everywhere and all I found is that I need to use Excel Solver. May I know how Solver can solve this question?

I have encountered a problem where linearizing a n with more than 1 term is almost impossible. After linearizing, I'm planning to graphical method to obtain Deff via gradient.

Someone please help.....

I want to solve PDE equation using Python. I have used codes of finite difference method for solving.

Could you suggest any solver Partial differential other than FiPy.

Hello,

My question is concerning the implementation of a parallel-plate waveguide (PPW) using 2D FDFD. I am using the total-field/scattered field method in the paper attached by Rumpf. One way to implement the PPW is to define two PEC objects (by modifying the epsilon matrix on the grid) and specify the total-field between the two objects using the Q matrix to excite the right modes. Is there a way to implement this where the PECs are defined as surfaces or boundary conditions instead of objects?

FEM, FTDT, MOM and BEM which method do you prefer and do use in your field?

Hello Dears

This problem is related to the MATLAB link with LUMERICAL.

I have used the MATLAB link feature with Lumerical software, Also in MATLAB, I have written a script for sweep Jsc according to the grating width of the relevant structure.

There is a FOR loop in MATLAB script, The output of the FOR loop for the first step is a reasonable value, And the outputs after the first stage are all zero,And the output of the last step is irrationally a repetition of the first step.

what is the problem?

I tried hard but I did not succeed.

Finally, I attached the MATLAB script.

Thank you in advance for your attention.

Motahari

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.

Hi dears

I want to do the absorption of a structure for the wavelength range of 280 to 900 with the desired divisions. For example, I want the wavelength distance in this case to be 0.5 nano, in other words, it returns the absorption information every 0.5 nano.

Lumerical(FDTD) apparently does this for random wavelengths. But I want to get the absorption for wavelengths of 280 to 900 nano, at distances of 0.5 nanometers.

In other words, in the image below, I want the value of "value", 0.5 Nano 0.5 Nano change.

Is there a way to do this in Lumerical(FDTD) ?

Thanks in advance for your reply.

Motahari

I am solving a transinet convection-diffusion equation

u_t + a*u_x - nu*u_xx = 0 in (0,1)

Taking,

Convection coefficient a = 1

Diffusion coefficient nu = 0.005

Number of elements = 100

I got Peclet number Pe = 1

For same case now,

Time step = 0.01

End time = 0.6

I got Courant number C = 1

I need following 4 conditions to fulfill.

1). C =1 and Pe = 5

2). C =1 and Pe = 100

3). C =3 and Pe = 5

4). C =3 and Pe = 100

My question is:

What should be the value of

"Convection coefficient a",

"Number of elements",

"Diffusion coefficient nu",

"Time step" and

"End time"

to get these 4 results separately.

Dear researchers

I hope that you are having good and healthy days

I am modeling a direct shear test using FLAC3D V6, the model actually works properly when it assigned to the elastic model, however, the same model does not reach the equilibrium if it switched into Mohr-Coulomb model to model pure sand (without cohesion c=0)

Have anyone of you guys faced the same problem?

Best,

Omar

I have used finite difference method to discretise the equation and have written a code for it on mathematica. Anyone knows how to write a code for the truncation error that is the order of accuracy? I am not very familiar with mathematica.

I have an one question which is :

What is a difference o relationship between layer-wise and zig-zag theories.

The finite difference method with Taylor expansion give a good accuracy higher order derivative of normal functions for which the expansion coefficients can be found following this link: https://en.wikipedia.org/wiki/Finite_difference_coefficient

My question is what would be the higher order expansion of the functional derivative knowing that it has a similar Taylor expansion. Please note that I'm talking about the numerical differentiation.

I am writing to inquire if there is a way to extract the inner surface info of a deformed geometry, and build a new part which can exactly fit into the space of the deformed geometry.

I am trying to model a cylindrical tank with fillers (e.g., sand) using the coupled temperature-displacement approach for thermomechanical stress analysis during the heating/cooling cycle (i.e., thermal ratcheting).

The model, solely composed of tank shell, is being heated from 399 ºF to 579 ºF. The result shows that the cylindrical tank shape at 399 ºF (top-left) expanded across the tank wall and a bit buckled towards the bottom of the tank (both top-right and bottom-right).

For now, I would like to fill this deformed tank with a continuum part (without a gap between the tank and the continuum part), and cool down this model from 579 ºF to 399 ºF. To this end, I created a new model and imported the deformed tank geometry at 579 ºF from the previous model. But I am having trouble making a part which would be exactly the same shape as the inner surface of the deformed tank (like a plaster mold casting (bottom-left).

I looked around the ABAQUS documentations/user community, but I couldn’t find any solutions. I would appreciate any input and advice you have on this problem.

I want to solve a 3D wave equations in curved coordinate (for 3D bent rib waveguide) numerically by finite difference method, but I don't know about convenient boundary conditions, which boundary conditions should be applied, Perfect Match Layer or Transparent boundary condition? could anyone help me please?

I have a problem of the form u_xx +a(x)u_x +b(x)u(x-\eta)+c(x)u(x+\gamma)=f(x)

with boundary(interval) conditions u(x)=\phi(x) on -\eta <= x<=0 and u(x)=\psi(x) on 1<= x<= 1+\gamma. where \eta and \gamma are constants. Is that possible to write the matlab code for this problem without using Taylor series expansion for the delay terms? If yes, please show me

Does anybody have experience with the Finite Difference Element Method described in http://www.scc.kit.edu/scc/docs/FDEM/Literatur/FDEM-Survey-Feb09.pdf and would advocate for or against using it? The method works on an unstructured grid, the field quantities are represented by their values at the grid points, and spatial derivatives are evaluated at the grid points by means of fitting polynomials into the gridpoints in the neightborhood of the respective gridpoint.

To me, at first sight, the method seems to have a couple of advantages, compared to FEM:

- The meaning of the state variables of the discretized system is intuitive

- It can be applied as a "black box" to virtually every PDE

- There is no a priori pen and paper work necessary for calculating weak forms, quadrature formulas etc.

- It can readily be extanded to rather high orders

- The PDE can contain arbitrarily high derivatives, in principle

- The error of the derivatives can be estimated

Does anyone know any drawbacks of the method?

I have practiced 2nd order FDM discretization technique for 2D Laplace and Poisson Equation but I am totally confused about how to get fourth-order discretization technique. I would be thankful for your spending your valuable time.

I read about the membrane and shear locking appearing in shell element. Most references explain the reasons for shear locking but do not provide sufficient explanations for membrane locking.

I would like to ask about the reasons why membrane locking appears in shell element formulation and how to solve it?

Thanks for reading.

Hi, currently I am looking for technical articles on droplet generation using FDM approach. What are the boundary and initial conditions adopted?

I have read a lot of papers regarding the implementation of the meshless finite difference method and I am also aware as to how to implement the derivative conditions for steady-state (non-time variant) calculations (I will solve the derivative matrix system and the natural boundary equation

*du/dn = f*in order to for a linear algebraic system that can calculate the derivatives and the value of*f*, then solve for the values of*u*that would force the value of f to be the desired value).My problem is how to implement such conditions should I desire to integrate the PDE with respect to time. How do I exactly do this?

As far as I understand, I cannot openly solve for dependent variable

*u*as there is an initial condition for*u*already, which means that the values of the derivatives are fixed already - and in return, there is a fixed value of*f*already.If I intend to force

*f*to be equal to the desired natural boundary condition, it would require me to change the values of*u*, which is again, not permissible as there are initial conditions. Thoughts?Which is the latest method to solve non linear equation using finite difference method.

Can you tell me some methods for solving non linear equations using finite difference method.

Dear researchers

Whether material exists or can exist that is not elastic but has a linear behavior?

In fact, the loading slope with the loading belt is not the same and has a strain remaining in the elastic range

i can solve analytically using method of separation of variables. but is finite difference method applicable to reach the numerical solution?

Dear my colleagues,

In recent days, I searched a lot to know that which cells size is most appropriate for numerical groundwater modeling (finite difference method). But I could find any reference. Could any help me in this regard. Thank you.

I'm looking for a numerical method to solve the space-fractional reaction-diffusion equation.

What is the best numerical method to solve 2D space-fractional partial differential equation?

Numerical Methods

Spectral element method

Finite element method

Finite Difference Method

Space-fractional Partial Differential Equations

In FE some elements are overlapping. I read a paper says thst such overlapping causes higher in plane stiffness only. I wonder does the impact on accuracy of solutions very big?

When using Return Mapping algorithm, I implement Newton–Raphson iteration to reach the value of plastic multiplier. I know that the total value of plastic multiplier should not be negative. But, what should I do if one increment of plastic multiplier in an iteration is negative. Should I stop iteration or continue or what?

Can any body suggest me any source code/software that can generate synthetic seismogram using using finite difference method.

I know about mesh density, skewness, wrap angles, and aspect ratio.

Per literature, aspect ratio is a quick tool to define quality of mesh.

Is there a rule of thumb for acceptable values of elements aspect ratio?

Is it possible to have a mixed mesh with plane elements(plane stress/strain) and bernoulli beams?For example if we have a CST element connecting with a beam at one node.In that case,in this node beam will have only axial displacements?(cause lateral displacements aquire C1 continuity and CST offers C0)Is that possible?

Dear friends

I have a serious problem in order to regenerate the results of the attached paper. I do exactly mentioned method (FEM) in the paper but I don't get correct results.

This paper about gas face seal and compressible zeroth and first order perturbed Reynolds equation. I Solved zeroth order with FEM and FDM correctly and I got same results that bring out in the paper (Opening force for various pressure ratio) and I solve first order equation with 1 pressure ratio (figure 5 and 6) (I am thankful to you if look at the paper), but in other figure I can't get the paper's results. I try many method to solve linear system of equation (Ax=b) such as direct method, iterative method (i.e. gauss-sidel, cgs, gmres, bicg, pcg ...) but I failed, also I try many network grid and there is no achievement.

So what should I do?

I really know my question is general, but I really don't know about the errors.

I have developed a honeycomb sandwiched structure in Salome platform, meshed with netgen 2D, then calculated the compression stresses on it using Calculix open source FE.

I tried to optimise the element offset in order to eliminate such problem.

Attached is the photo of the honeycomb core.

Hello RG users,

The rocks are recrystallized limestones and dolomites and physically in various conditions such as in some areas the outcrop is fresh and intact, in some areas it is lightly or highly decomposed and weathered, even somewhere there are residual soils. Also, some areas contain discontinuities and some not.

Assume that I have the plain 3D geometry. I simply cannot assume that the whole area is homogeneous and has same characteristics.

My question is How can I efficiently represent such varying conditions (heterogeneity) in a 3D model based on FEM, DEM, FDEM etc. ? Is there any software capable of doing it?

Thank you!

Best Regards,

Bekir SF

Most of the CFD solvers use FVM. However, FDM is pretty simple to implement. I am interested to know exactly what advantages do FVM offer. And when should one go for FDM if he is planning to write a code from scratch.

I've tried using the Concrete Damaged Plasticity parameters but the model just would not work. I'm trying to model a beam-column joint using ECC as the joint material (region intersection between beam and column) under reversed cyclic loading. But the non-linearity of the compression, tensile stress-strain curves of the developed concrete took processing time near 24 hours with an odb file close to 13GB, which is unworkable if trying to extract XY data. To make things worse, that was just an incomplete 1 cycle of a 24 full cycle loading.

Below is a picture of the simple model. The base of the column is pin supported and a displacement controlled load is imposed on the face of the beam at only z-direction (towards the beam) no rotation and displacement at x,y.

Is there an alternative way to model the ECC in abaqus? Or are there way to improve my model? Attached is the picture. Thank you in advance.