THIRD-ORDER UPWIND FINITE ELEMENT SIMULATION OF INCOMPRESSIBLE VISCOUS FLOWS

A Finite Element Method for Viscous Incompressible Thermal Flows

A finite element method for steady-state viscous incompressible thermal flows has been developed. The finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consists of the conservation of mass, momentum, and energy equations. These derived finite element equations are validated by developing a corresponding finite element computer program that can be ...

Least Squares Finite Element Methods for Viscous, Incompressible Flows

This paper is concerned with finite element methods of least-squares type for the approximate numerical solution of incompressible, viscous flow problems. Our main focus is on issues that are critical for the success of the finite element methods, such as decomposition of the Navier-Stokes equations into equivalent first-order systems, mathematical prerequisites for the optimality of the method...

Simulation of time-dependent compressible viscous flows using central and upwind-biased finite-difference techniques

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...

Incompressible Viscous Flows

In this article, we describe some approaches to the eecient numerical computation of viscous incompressible ows governed by the Navier-Stokes equations. We concentrate on laminar ows, stationary as well as nonstationary, for Reynolds numbers of moderate size, and in general domains. The emphasis is on spatial discretization by the nite element method. We discuss the treatment of the incompressi...