Recent advances in the development of implicit schemes for the equations of fluid dynamics
Abstract
Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of oneleg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the Pdimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.
 Publication:

Numerical Methods in Fluid Dynamics
 Pub Date:
 1981
 DOI:
 10.1007/3540106944_66
 Bibcode:
 1981LNP...141..429W
 Keywords:

 Computational Fluid Dynamics;
 Equations Of Motion;
 Flow Equations;
 Alternating Direction Implicit Methods;
 Boundary Conditions;
 Boundary Value Problems;
 Conservation Laws;
 Differential Equations;
 Gas Dynamics;
 Inviscid Flow;
 Linear Equations;
 Wave Equations;
 Fluid Mechanics and Heat Transfer