High-order splitting methods for the incompressible Navier-Stokes equations. (English) Zbl 0738.76050

A new pressure formulation for splitting methods is developed that results in high-order time-accurate schemes for the solution of the incompressible Navier-Stokes equations. In particular, improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods. A new family of stiffly stable schemes is employed in mixed explicit/implicit time-integration rules. These schemes exhibit much broader stability regions as compared to Adams-family schemes, typically used in splitting methods.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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