A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm

We have developed 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 Kurapatanko, and also contains a limiter designed to switch off the viscosity for shockless compression and rigid-body rotation. Mimetic discretizations are used to derive the form of the momentum and energy equations for a nonorthogonal grid where the viscosity tensor is evaluated at the zone edges. The advantage of the tensor viscosity is a reduction of the dependence of the solution on the relation of the grid to the flow structure.