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KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

Bojan Popov, Texas A&M University
Entropy Viscosity


  • Jean-Luc Guermod, Texas A&M University
  • Richard Pasquetti, Nice Sophia Antipolis University (France)
  • Bojan Popov, Texas A&M University


We introduce a new shock-capturing technique for solving nonlinear conservation laws. The method consists of adding a nonlinear viscosity to the Galerkin formulation of the nonlinear hyperbolic equation or system of equations. The key idea is that the added viscosity is proportional to the residual of the entropy equation and it is always limited from above by first order dissipation. The treatment of the nonlinear viscous term is explicit in time which makes the method very simple to implement for various discretizations: finite elements, spectral elements, and Fourier approximations. We prove that the method is convergent in some simple scalar cases and verify its performance numerically on various one and two dimensional benchmarks including scalar equations and nonlinear systems of conservation laws.