TwoPoint Implicit Scheme for Euler Equations
Abstract
A new twopoint implicit scheme for solving the Euler equations was developed, which is secondorder accurate in space and time. This is an extension of the MacCormack implicit scheme, and is taking account of the following points; 1. to solve for the physical quantity itself at a new timestep, not for change of the physical quantity in time, 2. to modify the implicit operators for stability so as not to decrease accuracy of the approximation of the first derivative. The resulting method is efficient and easy to program. This scheme was compared with various other schemes for a shock tube problem. No physically irrelevant pressure distributions of the shock wave obtained by the present method were observed. It was confirmed that the present one produced good results for a large CFL number.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 May 1983
 DOI:
 10.1143/JPSJ.52.1525
 Bibcode:
 1983JPSJ...52.1525O
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Finite Difference Theory;
 Shock Waves;
 One Dimensional Flow;
 Unsteady Flow;
 Fluid Mechanics and Heat Transfer