Implicit time dependent methods for inviscid and viscous compressible flows
Abstract
Linear multistep methods; predictorcorrector methods; centered implicit dissipation schemes; and characteristic modeling schemes for compressible flows are introduced. The multistep algorithm is unconditionally stable and the error on the converged steady solution does not depend on the time step used, but the short wavelengths are not damped and therefore the scheme is not dissipative in the sense of Kreiss. Dissipation is provided by appending explicit and implicit artificial viscosity. The predictorcorrector scheme is centered in space for a linear equation intrinsically dissipative without artificial viscosity and requires the solution of two block bidiagonal systems for each space variable. The implicit schemes are single step schemes with centered differencing in space. The time differencing produces the appropriate dissipation. For Euler equations, characteristic schemes produce the dissipation by noncentered discretization in space.
 Publication:

In its Introduction to Computational Fluid Dynamics 61 p (SEE N8627597 1834
 Pub Date:
 1985
 Bibcode:
 1985icfd.book.....D
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Inviscid Flow;
 Time Dependence;
 Viscous Flow;
 Dissipation;
 Euler Equations Of Motion;
 Flow Characteristics;
 NavierStokes Equation;
 Predictions;
 PredictorCorrector Methods;
 Fluid Mechanics and Heat Transfer