Journal ArticleDOI
A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems
TLDR
In this article, Petrov-Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation, and the addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the "unwinding", Petrov and Galerkin, finite element methods.Abstract:
In one dimension, Petrov—Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the ‘unwinding’, Petrov—Galerkin, finite element methods. The ‘balancing dissipation’ is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two-dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.read more
Citations
More filters
Journal ArticleDOI
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
Journal ArticleDOI
Comparison of some finite element methods for solving the diffusion-convection-reaction equation
TL;DR: It is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerskin method has a stabilization effect similar to a sub-grid scale model, which is in turn related to the introduction of bubble functions.
Journal ArticleDOI
Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations
TL;DR: In this paper, a Petrov-Galerkin finite element formulation for first-order hyperbolic systems of conservation laws with particular emphasis on the compressible Euler equations is presented.
Journal ArticleDOI
Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations†‡
TL;DR: The current status of streamline-upwind/Petrov-Galerkin (SUPG) methods for the analysis of flow problems is surveyed in an analytical review as mentioned in this paper.
Journal ArticleDOI
The solution of non‐linear hyperbolic equation systems by the finite element method
TL;DR: In this article, a finite element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated.
References
More filters
Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
An ‘upwind’ finite element scheme for two‐dimensional convective transport equation
Journal ArticleDOI
Finite element methods for second order differential equations with significant first derivatives
TL;DR: Asymmetric linear and quadratic basis functions are introduced and shown to overcome the difficulty ofGalerkin finite element methods in an appropriate two point boundary value problem.
Journal ArticleDOI
Tensor viscosity method for convection in numerical fluid dynamics
John K. Dukowicz,John D. Ramshaw +1 more
TL;DR: The tensor viscosity method as mentioned in this paper is a generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping.
Related Papers (5)
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more