Implicit finite difference simulation of inviscid and viscous compressible flow
Abstract
It is not always convenient to use the simplified equations which extract the essential physics from the more complete set of inviscid and viscous fluid conservationlawequations. Such a situation may occur if the usually inviscid outer flow is highly rotational and/or if the viscous layer is fully separated. The solution of a system of conservationlawequations of fluid flow may present certain problems. Characteristic speeds of disparate magnitude and of both positive and negative sign may be encountered. These conditions can make use of implicit differencing schemes desirable and put rather severe constraints on the choice of spatial differencing operators. The present study has the objective to review the use of implicit finite difference schemes to solve the Euler and NavierStokes equations in primitive variables. An approximate factorization implicit finite difference scheme for solving the Euler and NavierStokes equations is discussed. Ways of splitting and reducing the governing equations are also reviewed.
 Publication:

Transonic, Shock, and Multidimensional Flows: Advances in Scientific Computing
 Pub Date:
 1982
 Bibcode:
 1982tsmf.proc..181S
 Keywords:

 Computational Fluid Dynamics;
 Conservation Equations;
 Euler Equations Of Motion;
 Finite Difference Theory;
 Inviscid Flow;
 NavierStokes Equation;
 Viscous Flow;
 Airfoil Profiles;
 Conservation Laws;
 Error Analysis;
 Flow Distribution;
 Hyperbolic Differential Equations;
 Potential Flow;
 Rotating Fluids;
 Fluid Mechanics and Heat Transfer