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A tensor artificial viscosity using a mimetic finite differential algorithm. (English) Zbl 1002.76082
Summary: We develop a two-dimensional tensor artificial viscosity for finite difference shock wave computations. The discrete viscosity tensor is formed by multiplying the gradient of velocity tensor by a scalar term. The scalar term is based on the form of viscosity first presented by V. F. Kuropatenko [Proc. Steklov Inst. Math. 74 (1966), 116-149 (1967); translation from Tr. Mat. Inst. Steklov. 74, 107-137 (1966; Zbl 0168.46202)], and also contains a limiter designed to switch off the viscosity for shockless compression and rigid-body rotation. Mimetic discretizations are used to derive momentum and energy equations on nonorthogonal grid where the viscosity tensor is evaluated at zone edges. The advantage of tensor viscosity is a reduction of dependence of solution on the relation of grid to flow structure.

76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
Full Text: DOI
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