A split finite element algorithm for the compressible NavierStokes equations
Abstract
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the NavierStokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
 Publication:

Final Technical Report Tennessee Univ
 Pub Date:
 July 1979
 Bibcode:
 1979tenn.reptQ....B
 Keywords:

 Compressible Fluids;
 Finite Element Method;
 NavierStokes Equation;
 Algorithms;
 Computer Programs;
 Finite Difference Theory;
 Flow Distribution;
 Fluid Mechanics;
 Inviscid Flow;
 Iterative Solution;
 Linear Equations;
 Numerical Integration;
 Parabolic Differential Equations;
 Fluid Mechanics and Heat Transfer