A Mixed ExplicitImplicit Splitting Method for the Compressible NavierStokes Equations
Abstract
An application of both explicit and implicit operations in a timesplitting technique is carried out for viscous interaction studies between a laminar boundarylayer and an incident shock wave. The physical problem characterized by large local gradients near the wall demands a novel numerical technique that maintains accuracy and efficiency for stretched meshes. Specifically, the twodimensional NavierStokes equations are solved by a sequence of onedimensional operators, each being explicit or implicit for streamwise or normal coordinate operation, respectively. The explicit operator employs a noncentered scheme due to MacCormack. The implicit operator is of the Laasonen type and is secondorder accurate for nonuniform spacing. Both the explicit and mixed splitting techniques are evaluated using selected experimental data. The mixed technique is more economical and is free of nonlinear instabilities that plague the explicit one in the computation of extensive separated flows. Some discrepancies between the numerical and experimental results remain to be investigated as the theory tends to underpredict the size of the separation zone.
 Publication:

Some Methods of Resolution of Free Surface Problems
 Pub Date:
 1976
 DOI:
 10.1007/354008004X_330
 Bibcode:
 1976LNP....59..285L
 Keywords:

 Compressible Flow;
 Finite Difference Theory;
 Laminar Boundary Layer;
 NavierStokes Equation;
 Operators (Mathematics);
 Shock Wave Interaction;
 Error Analysis;
 Flow Stability;
 Run Time (Computers);
 Separated Flow;
 Splitting;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer