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Using the standard symmetry technique for applying boundary conditions forfree slip and flat walls with corners will lead to flow leak through the wallnear corners (violation of no penetration condition) and a corresponding errorin prediction of pressure. Also, prescribing a state at the corner as aboundary condition is not possible. In this paper, a method for tackling the`corner point state' problem is given and modifications to the standardsymmetry technique are proposed to mitigate flow leak near the corner. Usingthis modified symmetry technique, numerical solutions to the Euler equationsfor flows over forward facing and backward facing step are computed employingthe Shu-Osher conservative finite difference scheme with WENO-NP3reconstruction (with a formal order of accuracy in space of 3), Lax-Freidrichsflux splitting, and TVD-RK3 time discretisation. It is shown that using thismodified symmetry technique leads to mitigation of flow leak near the cornerand a better prediction of shock structure even on coarse meshes.

Modified symmetry technique for mitigation of flow leak near corners for compressible inviscid fluid flow