Spectral-finite element method for compressible fluid flows

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

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 ...

Least-squares Spectral Element Methods for Compressible Flows

This paper describes the application of the leastsquares spectral element method to compressible flow problems. The method is described and results are presented for subsonic, transonic and supersonic flow problems over a bump.

Gauge finite element method for incompressible flows

A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that aris...

An Edge Based Stabilized Finite Element Method For Solving Compressible Flows: Formulation and Parallel Implementation

This paper presents a nite element formulation for solving multidimensional compressible ows. This method is inspired by our experience with the SUPG, Finite Volume and Discontinuous-Galerkin methods. Our objective is to obtain a stable and accurate nite element formulation for multidimensional hyperbolic-parabolic problems with particular emphasis on compressible ows. In the proposed formulati...