A class of monotonic shockcapturing difference schemes
Abstract
Two principal approaches used in the numerical study of unsteady inviscid compressible flow problems  shockfitting and shockcapturing  are discussed briefly. This paper presents a new example of the latter approach. The proposed method is monotonic and provides secondorder accuracy in regions where the concept of order is meaningful. The method is simple and fast running. The monotonicity of a standard finite difference scheme (the wellknown MacCormack scheme was chosen in the paper) is achieved by means of a local conservative smoothing operation. It eliminated nonphysical ripples, which usually appear near discontinuities when nonmonotonic schemes are used. The method is similar to one developed by Boris and Book and gives essentially the same results, but is much simpler and faster. The proposed method is compared to some other finite difference schemes. Two one dimensional tests are used: a linear convection equation and a shock tube problem. Finally, the example of nonsteady threedimensional scattering of a shock wave by a step obstacle of finite width is discussed.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1981
 Bibcode:
 1981STIN...8214480Z
 Keywords:

 Compressible Flow;
 Finite Difference Theory;
 Gas Dynamics;
 Inviscid Flow;
 Shock Waves;
 Computational Fluid Dynamics;
 Shock Tubes;
 Three Dimensional Flow;
 Transport Properties;
 Fluid Mechanics and Heat Transfer