On a parabolic quadrilateral finite element for compressible flows

A quadratic finite volume element method for parabolic problems on quadrilateral meshes

In this paper we utilize affine biquadratic elements and a two-step temporal discretization to develop a finite volume element method for parabolic problems on quadrilateral meshes. The method is proved to have an optimal order convergence rate in L2(0, T ; H1(Ω)) under the ‘asymptotically parallelogram’ mesh assumption. Numerical experiments that corroborate the theoretical analysis are also p...

Discontinuous Galerkin Finite Element Method for Inviscid Compressible Flows

This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly ...

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Finite element simulation of compressible particle-laden gas flows

Amacroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Spec...

A nine-node quadrilateral FCBI element for incompressible fluid flows

We propose a nine-node ow-condition-based interpolation (FCBI) nite element for the analysis of 2D incompressible ows. Emphasis in the FCBI approach is on obtaining an element that is stable and can be used in rather coarse meshes even when considering high Reynolds number ows. The formulation of the element is presented and the results obtained in the solution of some test cases are given. Cop...