On a parabolic quadrilateral finite element for compressible flows

Abstract

We present a 9-node ®nite element for compressible¯ow solutions. A high-order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation. We give the solutions of various example problems to illustrate our experiences with the element. Ó

An adaptive mesh strategy for high compressible flows based on nodal re-allocation

“…7. It can be observed that the solution obtained with the initial mesh is close to the results obtained by Hendriana and Bathe (2000) with reference to the position of the shock wave as well as its intensity. Results obtained by Le Beau et al (1993) are not shown in Fig.…”

A comparison of several numerical methods for the solution of the Convection-Diffusion Equation using the method of finite spheres

“…This technique involves adding a higher order derivative artificial diffusion term to the Galerkin formulation for greater accuracy and stability [4],…”

“…The pure Galerkin formulation is realized in the limit of very fine discretization. In references [4,7,13] the factor C ¼ 1 9 was used for the one-dimensional FEM, derived analytically. The calculation of C for the MFS is more involved and is presented in Appendix A.…”

“…(13) are calculated. This derivation follows the one used by [4,7,13] to calculate their factor of C ¼ 1 9 for the Ho DAD method used with parabolic finite elements. The one-dimensional case that was used to determine the value of C, for a given nodal distribution and Peclet number, will be described.…”

“…The basic idea of upwind methods is to give upstream nodes more weight than downstream nodes, thus dealing more effectively with the convective terms. A few of the more popular upwind techniques are the Galerkin Least-Squares (GLS) method [2], the Streamline Upwind/Petrov Galerkin (SUPG) method [3] and the Higher Order Derivative Artificial Diffusion (Ho DAD) method [4].…”