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An efficient and robust implicit operator for upwind point Gauss-Seidel method. (English) Zbl 1123.76051
Summary: An efficient and robust implicit operator for the point Gauss-Seidel method is presented for solving the compressible Euler equations. The new implicit operator was derived by adding a scalar form of artificial dissipation to the upwind implicit side. The amount of artificial dissipation was locally adjusted using a weighting factor based on the solution gradient. For validation, the performance of the new implicit operator was compared in detail with that of several existing implicit operators which have been widely used for solving the flow equations. Numerical experiments showed that the stability and convergence characteristics of the new implicit operator are significantly better than those of other existing implicit operators for calculating flows ranging from subsonic to hypersonic speeds.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65F10 Iterative numerical methods for linear systems
Software:
Cobalt
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