Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Conservation properties of vectorial operator splitting
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
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We present a fully implicit finite difference method for the unsteady incompressible Navier-Stokes equations. It is based on the one-step @q-method for discretization in time and a special coordinate splitting (called vectorial operator splitting) for efficiently solving the nonlinear stationary problems for the solution at each new time level. The resulting system is solved in a fully coupled approach that does not require a boundary condition for the pressure. A staggered arrangement of velocity and pressure on a structured Cartesian grid combined with the fully implicit treatment of the boundary conditions helps us to preserve the properties of the differential operators and thus leads to excellent stability of the overall algorithm. The convergence properties of the method are confirmed via numerical experiments.