Prof. Dinshaw S. Balsara, from University of Notre Dame, USA, gave a lecture titled “HLLI Universal Riemann Solver for Conservative and Non-Conservative Hyperbolic Systems and its Multidimensional Extensions”at AMSS on 11, July, 2017.  

In recent years, they have seen a considerable need to accurately simulate all different types of hyperbolic systems. Usually, one wishes to use higher order Godunov methods for the solution of these systems. While many very useful hyperbolic systems can be cast in strictly conservation form, several very important hyperbolic systems have non-conservative products. Therefore, they need to have an efficient one-dimensional Riemann solver that can treat conservative as well as non-conservative hyperbolic systems within the same framework.  

In the first half of this talk, Prof. Dinshaw S. Balsara presented a simple, highly efficient Riemann solver that operates on conservative as well as non-conservative hyperbolic systems.In the second half of this talk, he extended the 1D HLLI Riemann solver to multidimensions. HLLI can resolve intermediate waves well. The Riemann solvers had been documented in the literature by Dumbser and Balsara (2016) JCP and Balsara and Nkonga (2017) JCP. This work was also described briefly in Appendix C on the author’s website: http://www.nd.edu/~dbalsara/Numerical-PDE-Course.