Current progress in solving the time-dependent, incompressible Navier-Stokes equations in three-dimensions by (almost) the FEM

Conference · Mon Mar 01 04:00:00 EST 1982

OSTI ID:5257180

Gresho, P M; Upson, C D

We have been pursuing the development of numerical methods which, while originally derived via the conventional Galerkin Finite Element Method (GFEM), have been significantly modified in the interest of cost-effectiveness to the point where we now refer to them as a useful blend of finite element and finite difference methods. Starting with the simplest 3-D isoparametric element and the simplest time integration method (explicit Euler), the principal modifications of GFEM are that the mass matrix is diagonalized via lumping and all Galerkin integrals are evaluated approximately using one-point quadrature. Additional gains in computational speed have been achieved by two modifications of the time integration method: i.e. the introduction of a procedure called subcycling, which permits less frequent updates of the pressure relative to the stability-limited processes of advection and diffusion, and the often expensively small time-step restriction required to assure numerical stability has been eased via the introduction of an additional anisotropic viscosity. The current status of this hybrid method is summarized, and sample numerical results are presented.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5257180
• Report Number(s): UCRL-87445; CONF-820631-1; ON: DE82012259
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
FLUID FLOW
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS