Extension of the entropy viscosity method to flows with friction forces and source terms

In this paper, we extend the entropy viscosity method to 1-D Euler equations with source terms present. The entropy viscosity method has been successfully applied to hyperbolic equations such as Burgers equation and the Euler equation system. This method consists in adding dissipative terms to the governing equations so as to ensure the entropy minimum principle. The dissipative terms contain a viscosity coefficient (function) that locally modulates the amount of dissipation. This viscosity coefficient is based on the entropy production that occurs in the wiggles, discontinuities, and shocks of hyperbolic equation systems. By adding source terms to the Euler equations (friction and gravity forces to the momentum equation and heat sources/sinks in the energy equation), the entropy viscosity method must be modified to account for the entropy production due to these additional terms. Tests are run for a 1D channel, using pressurized water reactor (PWR) conditions, with the RELAP-7 code based on the MOOSE framework. The equations are discretized with a continuous Galerkin finite element method (FEM) using linear polynomials along with a second-order, implicit temporal scheme (BDF2). (author)