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Approximate factorization as a high order splitting for the implicit incompressible flow equations. (English) Zbl 0760.76059
Summary: We apply the method of approximate factorization to derive a second-order accurate splitting of the incompressible flow equations (Stokes or Navier-Stokes equations). This is novel because the method of approximate factorization was believed inapplicable to this type of equation system. We demonstrate the resulting splitting on a second-order Crank-Nicolson discretization and point out its intimate relationship to some existing second-order accurate splitting (projection) methods. Further, we use the approximate factorization method to derive entirely new splittings. We first develop a new generalized second-order accurate splitting which may be specialized to a variety of applications. We indicate its applications to finite-elements, “checkerboard-free” cell-centered discretizations, and ocean modeling. We then generalize the original splitting to an arbitrary high-order scheme.

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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