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High-order accurate numerical pressure correction based on geometric multiGrid schemes for the incompressible navier-stokes equations

Mathioudakis Emmanouil, Mandikas Vasileios, Kampanis, Nikolaos A, John A. Ekarinaris

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Περίληψη

ForthenumericalsolutionofincompressibleNavier-Stokesequations using a high order accurate discretization method a global pressure correction method can applied. This is equivalently with the solution of a Poisson-type boundary value problem at each time step which is the most computationally intense procedure of the numerical method. In this work, several Multi-Grid schemes are developed for the numerical solution of the large and sparse linear system arising from the discretization of the Poisson-type pressure correction on staggered grids. Multigrid techniques are not straightforward in this case, because the coarse grid does not constitute part of the fine grid. Appropriate restriction and extension operators are designed for the efficient application of multigrid proce- dure. The performance investigation using the V-cycle, W-cycle and Full Multi- Grid algorithms, resulted that multigrid schemes can accelerate significantly the numerical solution process.

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