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

Orhan Mehmetoglu, Texas A&M University
Central-Type Schemes for Nonlinear Hyperbolic Conservation Laws


  • Orhan Mehmetoglu
  • Bojan Popov
  • Vladimir Tomov


Central-type schemes owe their efficiency to the fact that they do not require solutions of Riemann problems or computation of intercell fluxes. In this work, we consider two classes of such schemes: Nessyahu-Tadmor (NT) type schemes and an entropy viscosity method. First, we present a theoretical result in which a maximum principle for the NT scheme with the MAPR-like limiter in one dimension is proved. Then, we show that in two dimensions and for systems, numerical robustness is still observed, even if a theoretical result proving a maximum principle is still missing. To show that the proposed schemes capture the composite waves accurately, numerical results are presented for a number of hyperbolic systems of conservation laws (in 2D) with convex and non-convex fluxes. Future plans consist of combining these two methods into a non-staggered entropy-based high-order central-type scheme.