Yu Liu, Tulane University


New Adaptive Artificial Viscosity Method for Hyperbolic Systems of Conservation Laws

Abstract: We propose a new finite volume method for solving general multidimensional hyperbolic systems of conservation laws. Our method is based on an appropriate numerical flux and a high-order piecewise polynomial reconstruction. The latter is utilized without any computationally expensive nonlinear limiters, which are typically needed to guarantee nonlinear stability of the scheme. Instead, we enforce stability of the proposed method by adding a new adaptive artificial viscosity, whose coefficients are proportional to the size of the weak local residual, which is sufficiently at the shock regions, much smaller near the contact waves, and very small in the smooth parts of the computed solution.


Advisor: Alexander Kurganov, Tulane University