Prabir Daripa

Texas A&M University | TAMU · Department of Mathematics

Two distinct effects that polymers exhibit are shear thinning and viscoelasticity. The shear thinning effect is important as the polymers used in chemical enhanced oil recovery usually have this property. We propose a novel approach to incorporate shear thinning effect through effective dynamic viscosity of the shear thinning polysolution. The proc...

Two distinct effects that polymers exhibit are shear thinning and viscoelasticity. The shear thinning effect is important as the polymers used in chemical enhanced oil recovery usually have this property. We propose a novel approach to incorporate this shear thinning effect through an effective dynamic viscosity of the shear thinning polysolution....

We present a theoretical study on the role of elasticity in causing fingering or fracturing instability during the immiscible displacement process of a viscoelastic fluid by another viscoelastic fluid in a rectilinear Hele-Shaw cell. Upper convected Maxwell (UCM) models are used for both fluid layers and linear stability analysis is performed in th...

We theoretically study the linear stability of the Saffman-Taylor problem where a viscous Newtonian fluid (with viscosity ηl) displaces an Upper Convected Maxwell (UCM) fluid (with viscosity ηr) in a rectilinear Hele-Shaw cell. The dispersion relation is given by the roots of a cubic polynomial with coefficients depending on wavenumber along with s...

We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients and eigenvalue-dependent boundary conditions. We study this eigenvalue problem and find upper bounds on the s...

We use linear stability analysis to demonstrate how to stabilize multilayer radial Hele-Shaw and porous media flows with a time-dependent injection rate. Sufficient conditions for an injection rate that maintains a stable flow are analytically derived for flows with an arbitrary number of fluid layers. We show numerically that the maximum injection...

In this article, the convergence of a hybrid numerical method introduced in Daripa & Dutta (2017) (J. Comput. Phys., 335:249-282, 2017) has been established. This method integrates a discontinuous finite element method with a modified method of characteristics (MMOC) in combination with finite difference (FD) procedures, and has been successfully a...

In this article, the convergence of a hybrid numerical method introduced in Daripa & Dutta (2017) [11] has been established. This method integrates a discontinuous finite element method with a modified method of characteristics (MMOC) in combination with finite difference (FD) procedures, and has been successfully applied to solve a coupled system...

We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients and eigenvalue-dependent boundary conditions. We study this eigenvalue problem and find upper bounds on the s...

We study the stability of multi-layer radial flows in porous media within the Hele-Shaw model. We perform a linear stability analysis for radial flows consisting of an arbitrary number of fluid layers with interfaces separating fluids of constant viscosity and with positive viscosity jump at each interface in the direction of flow. Several differen...

We study the stability of multi-layer radial flows in porous media within the Hele-Shaw model. We perform a linear stability analysis for radial flows consisting of an arbitrary number of fluid layers with interfaces separating fluids of constant viscosity and with positive viscosity jump at each interface in the direction of flow. Several differen...

We develop analysis based fast and accurate {\bf direct} algorithms for several biharmonic problems in a unit disk derived directly from the Green's functions of these problems, and compare the numerical results with the ``decomposition" algorithms (see \cite{Aditidaripa1}) in which the biharmonic problems are first decomposed into lower order prob...

Chemical enhanced oil recovery by surfactant-polymer (SP) flooding has been studied in two space dimensions. A new global pressure for incompressible, immiscible, multicomponent two-phase porous media flow has been derived in the context of SP flooding. This has been used to formulate a system of flow equations that incorporates the effect of capil...

Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in...

In this work, we present several computational results on the complex biharmonic problems. First, we derive fast Fourier transform recursive relation (FFTRR)-based fast algorithms for solving Dirichlet- and Neumann-type complex Poisson problems in the complex plane. These are based on the use of FFT, analysis-based RRs in Fourier space, and high-or...

We consider a non-standard eigenvalue problem arising in stability studies of 3-layer immiscible porous media and Hele-Shaw flows which contain the viscous profile of the middle layer as a coefficient in the eigenvalue problem. We characterize the eigenvalues and eigenfunctions of this eigenvalue problem. We then apply this characterization to an e...

We present a non-standard eigenvalue problem that arises in the linear stability of a three-layer Hele-Shaw model of enhanced oil recovery. A nonlinear transformation is introduced which allows reformulation of the non-standard eigenvalue problem as a boundary value problem for Kummer's equation when the viscous profile of the middle layer is linea...

Motivated by stability problems arising in the context of chemical enhanced oil recovery, we perform linear stability analysis of Hele-Shaw and porous media flows in radial geometry involving an arbitrary number of immiscible fluids. Key stability results obtained and their relevance to the stabilization of fingering instability are discussed. Some...

This paper evaluates the relevance of Hele-Shaw (HS) model based linear stability results to fully developed flows in enhanced oil recovery (EOR). In a recent exhaustive study [Transport in Porous Media, 93, 675-703 (2012)] of the linear stability characteristics of unstable immiscible three-layer “Hele-Shaw” flows involving regions of varying visc...

Saffman-Taylor instability is a well known viscosity driven instability of an interface separating two immiscible fluids. We study linear stability of displacement processes in a Hele-Shaw cell involving an arbitrary number of immiscible fluid phases. This is a problem involving many interfaces. Universal stability results have been obtained for th...

In this paper, we discuss a previously unknown selection principle of optimal viscous configurations for immiscible multi-fluid Hele-Shaw flows that have emerged from numerical experiments on three- and four-layer flows. Moreover, numerical investigation on four-layer flows shows evidence of four-layer systems which are almost completely stabilizin...

Stabilization of multi-layer Hele-Shaw flows is studied here by including the influence of Rayleigh–Taylor instability in our earlier work (Daripa, J. Stat. Mech. 12:28, 2008a) on stabilization of multi-layer Saffman–Taylor instability. Furthermore, this article goes beyond our previous work with few extensions, improvements, new interpretations, a...

We have recently developed two quasi-reversibility techniques in combination with Euler and Crank-Nicolson schemes and applied successfully to solve for smooth solutions of backward heat equation. In this paper, we test the viability of using these techniques to recover non-smooth solutions of backward heat equation. In particular, we numerically i...

In enhanced oil recovery by chemical flooding within tertiary oil recovery, it is often necessary to choose optimal viscous profiles of the injected displacing fluids that reduce growth rates of hydrodynamic instabilities the most thereby substantially reducing the well-known fingering problem and improving oil recovery. Within the three-layer Hele...

In this paper, we consider the problem of control of hydrodynamic instability arising in the displacement processes during enhanced oil recovery by SP-flooding (Surfactant–Polymer). In particular, we consider a flooding process involving displacement of a viscous fluid in porous media by a less viscous fluid containing polymer and surfactant over a...

With the motivation of understanding the effect of various injection policies currently in practice for chemical enhanced oil recovery, we study linear stability of displacement processes in a Hele-Shaw cell involving injection of an arbitrary number of fluid phases in succession. This work mainly builds upon our earlier study of the three-layer ca...

Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel...

We numerically investigate the optimal viscous profile in constant time injection policy of enhanced oil recovery. In particular, we investigate the effect of a combination of interfacial and layer instabilities in three-layer porous media flow on the overall growth of instabilities and thereby characterize the optimal viscous profile. Results base...

We consider the linear stability of three-layer Hele-Shaw flows with each layer having constant viscosity and viscosity increasing in the direction of a basic uniform flow. While the upper bound results on the growth rate of long waves are well known from our earlier works, lower bound results on the growth rate of short stable waves are not known...

Stability theory plays a major role from fundamental science to applied sciences. It is useful in the design of many processes and engineering instruments as well as in explaining many phenomena. In this paper we review some of the author's and his collaborator's recent works on the extension of Saffman-Taylor instability which occurs at an interfa...

In this letter we investigate the effect of interfacial surfactant on the motion of an air bubble rising in a vertical capillary tube filled with a viscous fluid and sealed at one end. A thin layer of liquid, with almost constant thickness b, exists between the bubble interface and the tube wall. The fluid displaced by the front meniscus flows down...

This paper presents results of some numerical experiments on the backward heat equation. Two quasi-reversibility techniques, explicit filtering and structural perturbation, to regularize the ill-posed backward heat equation have been used. In each of these techniques, two numerical methods, namely Euler and Crank–Nicolson (CN), have been used to ad...

We will present numerical solutions from initial value calculations of a model of shallow water wave equation. For small data, numerical solution develops singularity in a finite time. Driven by the structure of solutions, we carry out analysis based on numerical results to prove singularity formation. Numerical and theoretical results will be show...

Current work is in progress on numerical investigation of the effect of variable viscosity profiles of internal layers on the stabilization of multi-layer Hele-Shaw flows. Our findings will be presented and compared, to the extent possible, with theoretical results available. Effect of diffusion on this stabilization may also be presented. This tal...

In a recently published article of Daripa and Pasa [Transp. Porous Media (2007) 70:11-23], the stabilizing effect of diffusion in three-layer Hele-Shaw flows was proved using an exact analysis of normal modes. In particular, this was established from an upper bound on the growth rate of instabilities which was derived from analyzing stability equat...

In experiments involving slow steady motion of a long finite bubble of fluid with very small viscosity in a capillary tube filled with a liquid of viscosity μ, a thin film of liquid of uniform thickness adheres to the tube walls between the front and the rear menisci of the bubble. Taking the contact angle of the liquid at the walls as zero and neg...

We consider two problems in complex fluids: (i) thickening of thin films in the Landau-Levich problem [1] of dip coating and in motion of long bubbles in capillary tubes [2]. In both of these problems, thickening of thin films is observed experimentally in the presence of interfacial surfactants which has been confirmed experimentally. Considering...

In this talk, we give a theoretical proof of the thickening effect of surfactant by considering a small concentration of surfactant gamma and variable surface tension on a long bubble interface which is moving slowly and steadily in a capillary tube filled with a liquid of viscosity mu. The contact angle is taken as zero at the walls and the gravit...

In experiments involving dip coating flows on an infinite flat substrate which is withdrawn from an infinite liquid bath, the thin film deposited far up on the plate usually thickens in the presence of insoluble interfacial surfactant. Using perturbation analysis within the lubrication approximation we prove that the film thickens in the presence o...

Upper bound results on the growth rate of unstable multi-layer Hele-Shaw flows are obtained in this paper. The cases treated are constant viscosity layers and variable viscosity layers. As an application of the bound, we obtain some sufficient conditions for suppressing instability of two-layer flows by introducing an arbitrary number of constant v...

We consider a setup in a Hele-Shaw cell where a fluid of constant viscosity l occupying a near-half-plane pushes a fluid of constant viscosity l occupying a layer of length L which in turn pushes another fluid of constant viscosity r occupying the right half-plane. The fluid upstream has a velocity U. Careful analysis of the dispersion relation ari...

Hydrodynamic instability in immiscible porous media flows in the presence of capillarity is investigated here. The analysis and arguments presented here show that the slowdown of instabilities due to capillarity is usually very rapid which makes the flow almost, but not entirely, stable. The profiles of the stable and unstable waves in the far-fiel...

We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed...

In this talk, we will provide some results in the context of multi-layer Hele-Shaw flows. We will address issues related to collective effects of individually unstable interfaces on the overall stability of multi-layer Hele-Shaw flows in the presence of interfacial surface tensions. We will also discuss complications in the analysis resulting from...

In this paper, we give a simple proof of the thickening effect of surfactant on the thin film deposited when a flat plate is withdrawn from a liquid bath. This problem without the effect of surfactant was first considered in the seminal paper of Landau and Levich (1942). Our proof here is based on an asymptotic analysis of the lubrication model for...

We will discuss some stability problems of two-phase flows in Hele-Shaw cell and porous media and provide some stability results based on Darcy's law and saturation model. Effects of surface tension in Hele-Shaw flows and capillarity in porous media flows on slowdown of instabilities will be quantified within linear theory. Results on hydrodynamic...

A brief review of our fast algorithms is given in this short paper. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the presence of diffusion, stability of three-layer Hele-Shaw flows which models enhanced oil recovery processes by polymer flooding is studied for the case of variable viscosity in the middle layer. This leads to the coupling of the momentum equation and the species advection-diffusion equation the hydrodynamic stability study of which is prese...

The upper bound results on the growth rates in unstable multi-layer Hele-Shaw flows will be derived. The cases treated are constant viscosity layers and variable viscosity layers. The upper bound provides a way to assess cumulative effects of many layers and many interfaces on the growth rates of unstable waves. As an application of the bound, we o...

We study the dip coating flow on a flat plate which is being withdrawn from a liquid bath. This problem was considered in the seminal paper of Landau and Levich (1942). A similar problem, concerning the motion of long bubbles in capillary tubes was considered by Bretherton (1961). In both problems, it is important to study the effects produced by i...

Standard perturbation methods are applied to Euler's equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α=a/h0, and long-wavelength parameter, β=2(h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0...

The stability of three-layer Hele-Shaw flows with middle layer having either constant or variable viscosity will be considered in this talk. We solve this problem for the case of constant viscosity exactly and obtain several results all of which are independent of the length of the middle layer: (i) a necessary and sufficient condition for instabil...

An upper bound on the growth rate of disturbances in three-layer Hele-Shaw flows with the middle layer having a smooth viscous profile is obtained using a weak formulation of the disturbance equations. A recently reported approach for the derivation of this bound is tedious, cumbersome, and requires numerical analysis. In contrast, the present appr...

We consider the problem of displacement processes in a three-layer fluid in a Hele–Shaw cell modeling enhanced processes of oil recovery by polymer flooding. The middle layer sandwiched between water and oil contains polymer-thickened water. We provide lower bounds on the length of the intermediate layer and on the amount of polymer in the middle l...

The problem of existence of trapped waves in fluids due to a cylinder is investigated for the hydrodynamic set-up which involves a horizontal channel of infinite length and depth and of finite width containing three layers of incompressible fluids of different constant densities. The set-up also contains a cylinder which is impermeable, fully immer...

The linear stability of three-layer Hele–Shaw flows with middle-layer having variable viscosity is considered. Based on application of the Gerschgorin’s theorem on finite-difference approximation of the linearized disturbance equations, an upper bound of the growth rate is given and its limiting case for the case of constant viscosity middle-layer...

The stokes flow involving a hybrid droplet submerged in an immiscible liquid was investigated. It was found that the drag force varyies significantly with respect to the two radii associated with the two-sphere geometry of the droplet, and the viscosity ratio of the two liquids in the continuous and dispersed phases. It was observed that in the cas...

Forced displacement of oil by polymer flooding in oil reservoir is one of the effective methods of enhanced (tertiary) oil recovery. A classical model of this process within Hele-Shaw approximation involves three-layer fluid in a Hele-Shaw cell having a variable viscosity fluid in the intermediate layer between oil and water. The goal here is to fi...

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast al...

We consider an axisymmetric flow of a thin liquid film on a rotating annular disk. The effects of surface tension and gravity terms are included. An asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the film thickness in comparison to the inner...

The Euler’s equations describing the dynamics of capillary-gravity water waves in two-dimensions are considered in the limits of small-amplitude and long-wavelength under appropriate boundary conditions. Using a double-series perturbation analysis, a general Boussinesq type of equation is derived involving the small-amplitude and longwavelength par...

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. This method can be easily extended to three-dimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which the arbitrary domain is embedded. A periodic solutio...

A class of model equations that describe the bi-directional propagation of small amplitude long waves on the surface of shallow water is derived from two-dimensional potential flow equations at various orders of approximation in two small parameters, namely the amplitude parameter α=a/h0 and wavelength parameter β=(h0/l)2, where a and l are the act...

The paper briefly describes some essential theory of a numerical method based on domain embedding and boundary control to solve elliptic problems in complicated domains. A detailed account of this method along with many proofs and numerical results can be found in Badea and Daripa.

In this paper, we extend the work of Daripa et al. [14–16,7] to a larger class of elliptic problems in a variety of domains. In particular, analysis-based fast algorithms to solve inhomogeneous elliptic equations of three different types in three different two-dimensional domains are derived. Dirichlet, Neumann and mixed boundary value problems are...

We consider the axisymmetric flow of a Newtonian fluid associated with the spreading of a thin liquid film on a rotating annular disk. The effects of surface tension and gravity terms are included. The asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characte...

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two...

Steady two-dimensional creeping flows induced by line singularities in the presence of an infinitely long circular cylinder with stick-slip boundary conditions are examined. The singularities considered here include a rotlet, a potential source and a stokeslet located outside a cylinder and lying in a plane containing the cylinder axis. The general...

this paper, we present efficient sequential and parallel algorithms for solving the Poisson equation on a disk using Green's function method

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999) 159]. Motivated by their work, we formally derive this equation from two-dimensional potential flow equations governing the small amplitude long capillary-gravity waves on the surface of shallow water for Bond nu...

The circle and sphere theorems in classical hydrodynamics are generalized to a composite double body. The double body is composed of two overlapping circles/spheres of arbitrary radii intersecting at a vertex angle �/n,n an integer. The Kelvin's transformation is used successively to obtain closed form expressions for several flow problems. The pro...

In this paper, the two-dimensional Stokes flow inside and outside a circular cylinder induced by a pair of line singularities (rotlet and stokeslet) is studied. Analytical solutions for the flow field are obtained by straightforward application of the Fourier method. The streamline patterns are sketched for a number of special cases where the cylin...

Two-dimensional Stokes flows generated by line singularities inside a circular cylinder are studied in the presence of stick-slip boundary conditions. For simplicity, line singularities are assumed to be parallel to the cylinder axis, all axes in the same plane. The interior boundary value problem associated with these flows is solved in terms of a...

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [Jour. Comput. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompre...

Exact analytical solutions are found for the steady state creeping flow in and around a vapor-liquid compound droplet, consisting of two orthogonally intersecting spheres of arbitrary radii (a and b), submerged in axisymmetric extensional and paraboloidal flows of fluid with viscosity (1) . The solutions are presented in singularity form with the i...

In this paper, we propose a domain embedding method associated with an optimal boundary control problem with boundary observations to solve elliptic problems. We prove that the optimal boundary control problem has a unique solution if the controls are taken in a finite dimensional subspace of the space of the boundary conditions on the auxiliary do...

Exact analytical solutions for steady-state axisymmetric creeping flow of a viscous incompressible fluid in the presence of a compound multiphase droplet are derived. The two spherical surfaces constituting a vapor-liquid compound droplet are assumed to overlap with a contact angle π/2. It is further assumed that the surface tension forces are suff...

We discuss two-dimensional slow viscous flow (Stokes flow) problems around a long infinite circular cylinder. The flows are assumed to be generated by line singularities of various types in the presence of a cylinder. The types of primary singularities considered here include (i) rotlets; (ii) stokeslets; and (iii) potential source/sink. Exact solu...

The problem of a plane bubble rising in a 2-D tube is revisited using Birkho#'s (1957) formulation. The equations in this formulation have a one parameter (Froude number F ) family of solutions which are divided into three regimes characterized by distinct topologies at the apex. These equations are solved numerically using a conventional series re...

The complicated nature of singularities associated with topological transition in the plane Taylorbubble problem is briefly discussed in the context of estimating the speed of the fastest smooth Taylorbubble in the absence of surface tension. Previous numerical studies were able to show the presence of a stagnation point at the tip of the bubbles f...

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159-207]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Bond number less than but very close to 1/3. On the basis...

The mathematical foundation of an algorithm for fast and accurate evaluation of singular integral transforms was given by Daripa [9,10,12]. By construction, the algorithm offers good parallelization opportunities and a lower computational complexity when compared with methods based on quadrature rules. In this paper we develop a parallel version of...

We study a sixth-order Boussinesq equation which describes bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Bond number less than but very close to 1/3. On the basis of far-field analyses and heuristic arguments, we show that the traveling wave solutions of this equation are weakly n...

Mathematical properties of a new class of model equations that describe two-way propagation of small amplitude long capillary-gravity waves on the surface of water are studied. From these equations, appropriate equations to model solitary waves in two cases, namely (I) when the Bond number tau and the amplitude parameter beta satisfies beta

We consider an ill-posed Boussinesq equation which arises in shallow water waves and nonlinear lattices. This equation has growing and decaying modes in the linear as well as nonlinear regimes, and its linearized growth rate σ for short-waves of wavenumber k is given by σ∼k 2 . Previous numerical studies have addressed numerical difficulties and co...

Local and non-local solitary waves of Boussinesq equations are considered. According to the classical weakly nonlinear theory of water waves, an illposed Boussinesq equation governs the propagation of long waves to leading order approximation and admits localized solitary wave solutions. The severe short wave instability of this equation casts real...

A parallel version of a fast algorithm for singular integral transforms (6) is presented. The parallel version only utilizes a linear neighbor- to-neighbor communication path which makes the algorithm very scalable and suitable for any dis- tributed memory architecture.

. A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a...

. Fast algorithms for the accurate evaluation of some singular integral operators that arise in the context of solving certain partial differential equations within the unit circle in the complex plane are presented. These algorithms are generalizations and extensions of a fast algorithm of Daripa (SIAM J. Sci. Stat. Comput., 13, No. 6, (1992), 141...

Introduction The Taylor-bubble problem consists of two fluids: a gas of negligible density in the interior of the bubble and an incompressible non-viscous fluid in the exterior of the bubble. The bubble is symmetric and infinitely long which rises under gravity at a speed U through a tube of width h. The dimensionless speed of the bubble is known a...

. Some useful filtering techniques for computing approximate solutions of illposed problems are presented. Special attention is given to the role of smoothness of the filters and the choice of time dependent parameters used in these filtering techniques. Smooth filters and proper choice of time dependent parameters in these filtering techniques all...

A combustion model using three mixture fractions has been developed for accurate simulation of coal:manure combustion. This model treats coal and manure off gasses separately. This model has been incorporated into the PCGC-2(Pulverized Coal Gasification and Combustion - 2 Dimensional, from Brigham Young University) code. Numerical results of this s...

Plane Taylor bubbles with correct and incorrect tip angles are numerically generated for the case of zero surface tension (s.t.) using a Fourier collocation method. We find that all of these bubbles satisfy correct asymptotic shape at their tails. We have identified some generic patterns in the behavior of these bubbles with incorrect tip angles. W...

In the past pointed bubbles have been obtained numerically in the presence of surface tension. In this paper it is proven that if such pointed bubbles do exist in the presence of surface tension, then the singularity at the corner must be an irregular singular point. The generality and significance of the result are discussed.

Two algorithms are provided for the fast and accurate computation of the solution of Beltrami equations in the complex plane in the interior of a unit disk. There are two integral operators which are fundamental in the construction of this solution. A fast algorithm to evaluate one of these integrals is given by Daripa (SIAM J. Sci. Stat. Comput.,...

An algorithm is provided for the fast and accurate computation of the solution of nonhomogeneous Cauchy–Riemann equations in the complex plane in the interior of a unit disk. The algorithm is based on the representation of the solution in terms of a double integral, some recursive relations in Fourier space, and fast Fourier transforms. The numeric...