Finite elements for fluid dynamics
Abstract
The first two parts of this report wind up a few questions in the mathematical formulation of vector fields governed by conservation and rotationality laws, with explicit application to fluid dynamic fields, possibly with shock waves. The points treated have a strong bearing on computational schemes and the stability of numerical calculations and the results provide a priori information on the way to select the appropriate set of equations, the right functional, and the most promising approximation space for finite element discretizations. The last assertion is then tested for the tricomi equation in a nonuniformly elliptic domain. A mixed Tricomi problem is discretized by an alternative collocation scheme which proves to be acoustic and stable as demonstrated on a few testcases. The collocation finite difference schemes have proven superior thus to the finite elements for this case. They are, however, more specialized and natural for linear problems and simple geometries. The variationally based finite elements, on the other hand, hold a better promise for complex geometries, and for an accurate treatment of shocks.
 Publication:

Final Report
 Pub Date:
 August 1980
 Bibcode:
 1980taui.rept.....G
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Shock Waves;
 Boundary Value Problems;
 Matrices (Mathematics);
 Random Variables;
 Fluid Mechanics and Heat Transfer