Finite difference schemes derived from the integral theorems of fluid mechanics
Abstract
A family of difference schemes is derived from the integral theorems for inviscid, compressible fluid flow. The theorems are formulated for a control volume in spacetime coordinates using the conservation form. Finite element techniques are used to approximate the volume integrals. In this paper, only triangular and tetrahedral shapes are used as basic elements and more complicated control volumes are constructed with a number of these basic elements. The principal advantages of this approach are: (1) The mesh geometries can be chosen to fit the boundaries; (2) The mesh is allowed to deform in time, thus accommodating moving boundaries and shock waves; (3) The schemes allow shock fitting or shock capturing; (4) Both explicit and implicit schemes can be derived with this method. In this paper, only explicit schemes are discussed.
 Publication:

9th Fluid and Plasma Dynamics Conference
 Pub Date:
 July 1976
 Bibcode:
 1976fpdy.confQ....T
 Keywords:

 Compressible Flow;
 Finite Difference Theory;
 Fluid Mechanics;
 Inviscid Flow;
 Finite Element Method;
 Shock Waves;
 Steady Flow;
 Supersonic Flow;
 Three Dimensional Flow;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer