A Characteristic Nonreflecting Boundary Condition for the Multidimensional Navier-Stokes Equations

概要

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Because the computational resources are finite, one needs to truncate the computational domain when he/she simulates a physical problem. This truncation gives rise to non-physical artificial boundaries and one cannot obtain proper solutions unless appropriate boundary conditions on such boundaries are imposed. Practically nonreflecting boundary conditions, which are boundary conditions that prevent the generation of reflections, are of great importance. By the reason of the practical robustness and the simplicity of implementation, the Poinsot-Lele boundary condition is one of the most popular methods for the Navier-Stokes equations right now. Their method is based on Thompson's boundary condition for the Euler equations, which, however, is essentially one-dimensional. Therefore the Poinsot-Lele boundary condition is valid only when the flow is perpendicular to the boundary theoretically. Here we propose a nonreflecting boundary condition for the Euler equations which does not have the assumption on the direction of flow. We also discuss its extension to the Navier-Stokes equations. Our basic idea is to estimate the direction of the flow from numerical data.
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