A critical review of numerical solution of NavierStokes equations
Abstract
The paper examines the chief problems encountered in obtaining solutions to the partial differential equations of fluid dynamics through numerical integration. The problem of the wellposedness of the differential and the difference equations and the problem of computational stability of a set of difference equations are studied. The application of the von Neumann analysis for the stability of numerical integration of the NavierStokes equations is discussed. The application of implicit difference algorithms is examined, with attention given to iterative methods in particular. The problem of conservative difference formulation is discussed, and general methods for heuristic error estimate are outlined. The problems in dealing with shock waves, artificial viscosity and shockinduced oscillations are also reviewed.
 Publication:

Progress in Numerical Fluid Dynamics
 Pub Date:
 1975
 DOI:
 10.1007/3540074082_2
 Bibcode:
 1975LNP....41...78C
 Keywords:

 Computerized Simulation;
 NavierStokes Equation;
 Convergence;
 Differential Equations;
 Error Analysis;
 Finite Difference Theory;
 Fluid Dynamics;
 Heuristic Methods;
 Iterative Solution;
 Numerical Stability;
 Shock Wave Propagation;
 Steady State;
 Supersonic Flow;
 Fluid Mechanics and Heat Transfer