Development of a nonreflecting boundary condition based on the Riemann invariant manifold

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Nonreflecting boundary conditions are of importance in numerical simulations of compressive fluid. In this research I developed a new nonreflecting boundary condition based on the Riemann invariant manifold. An improvement of this boundary condition was found to be same as Thompson's boundary condition, and this provided a new derivation of Thompson's boundary condition and a stability analysis. Researches on the discrete variational method are also performed in order to stabilize this boundary condition. As a result, some extensions of the discrete variational method are achieved.