Application of the volume penalization method to high-order accurate numerical scheme

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  • Volume Penalization法の高次精度スキームへの適用(数値計算(1),一般講演)

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The volume penalization method is one of applicable means to investigate numerically flows with complicated geometrical boundaries. In this study we research the behaviors of numerical errors occuring with the addition of volume penalization (VP) term to one-dimensional Burgers' equation, using 4th-order compact schemes in spacial discretization and the 4th-order runge-kutta method in time development. The volume penalization term has a mask function χ(x) describing boundary geometries and a parameter η called permeability. We adopted the step function as the χ(x) and changed the η from 10^<-2> to 10^<-5>. The results show that the numerical errors for Burgers' equation with VP term are much larger than that for it without one. The error becomes minimum at a number of grid points N which depend on η.


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