Solving Linear Diffusion-Reaction Networks in Porous Catalyst Particles using BEM

Multiple dioeusion reactions are frequently encountered in the modeling of heterogeneous catalytic reactors. Obtaining an accurate estimate of the yield and selectivity in such reactions is crucial for an optimal design of reactors. Due to the inadequacy of analytical techniques in handling non-uniform catalyst shapes and mixed boundary conditions, numerical techniques are often employed to compute these design parameters. Among other numerical techniques, the boundary element method (BEM) is a superior method to solve linear diffusion reaction problems. The integral nature of the BEM formulation allows for boundary only discretization of the particle thus reducing the computer execution time and the data preparation eoeort. In this work, a boundary element algorithm is developed to solve a network of linear dioeusion reactions in porous catalyst particles in two dimensions. For this purpose a matrix of fundamental solutions is defined and derived. The developed algorithm is applied to ..

Orthogonal Collocation in the Non-Conforming Boundary Element Method

This paper outlines the use of non-conforming (discontinuous) elements in the collocation boundary element method for solving two dimensional potential and Poisson type problems. The roots of an orthogonal polynomial (shifted Jacobi polynomial) are used as the collocation points. This results in increased accuracy due to the least square minimization property of the orthogonal polynomials. The advantage of using non-conforming elements is realized when the method is applied (i) to problems with singularities (both due to geometry and boundary conditions) and (ii) in conjunction with domain decomposition techniques. Also, the collocation points can be relocated within an element by changing two user defined parameters in the shifted Jacobi polynomial, thus providing an error indicator which can be used for mesh refinement purposes. This technique, called the rh method, is discussed and illustrated. The results obtained by using non-conforming boundary elements for standard test problems a..

Radial Basis Function Approximation in the Dual Reciprocity Method

The Dual Reciprocity Method (DRM) is a class of boundary element techniques wherein, the domain integral resulting from the non-homogeneous terms in Poisson type equations is transferred to equivalent boundary integral by using suitable approximation functions. The use of radial basis functions (RBF) as approximating functions for this purpose has several advantages over conventional interpolation techniques. In this work the convergence property of RBF, for two dimensional problems, is examined numerically. The interpolation error is quantified for a particular test function and the local behavior of the RBF is illustrated. The RBF are then used for approximation in DRM to solve non-linear Poisson type equations and the results are compared with known exact solutions. The close agreement of the numerical solution to the exact solution, for a uniform mesh refinement, demonstrates the convergence properties of the RBF and the accuracy of their use in DRM

Augmented Thin Plate Spline Approximation in DRM

The dual reciprocity method (DRM) is a popular mathematical technique to solve non-homogeneous Poisson type equations. The method involves the approximation of the non-homogeneous term by a set of radial basis functions (RBF) and transferring the resultant domain integral to an equivalent boundary integral. In this work, the augmented thin plate spline (ATPS) is shown to be superior to the frequently used linear RBF for DRM approximation in two dimensions. Comparison of the DRM implementation with augmented and unaugmented thin plate spline is also provided. Keywords: Dual reciprocity method, Boundary element method, Radial basis functions, Augmented radial basis functions, Thin plate spline i 1 Introduction The dual reciprocity method (DRM) is a class of boundary element methods (BEM) to solve non-homogeneous partial dioeerential equations (PDE), often referred to as Poisson type equations. In this method, the domain integral resulting from the non-homogeneous term, denoted as b, i..

Quasilinear Boundary Element Method for Nonlinear Poisson Type Problems

A novel boundary element procedure called the Quasilinear Boundary Element Method (QBEM) is developed to solve two dimensional non-linear Poisson type problems. The forcing function of the Poisson type equation is linearized and the resulting terms are transferred to the boundary using a fourth order transformation. This results in boundary only discretization and thus retains all the advantages of the BEM for linear problems. The method provides extremely accurate results for mildly non-linear forcing functions. For strongly non-linear forcing functions, the method is used at a subdomain level and produces good results with only a few subdomains. The method is illustrated by a few test cases and the results compare favorably with solutions obtained through known methods such as the dual reciprocity method (DRM)