#### Abstract

In this talk we discuss about certain numerical methods together with its analysis for hyperbolic conservation laws (CL) and conservation laws with discontinuous (CL-DF). As examples we choose Euler equations of gas dynamics, two-phase flow in porous media, multi-componet flow transport in enhanced oil recovery etc. In the first half we give a brief introduction to both theoretical and numerical aspects of CL and CL-DF. Followed by this we present the convergence analysis of a second order scheme to the physically relevant (entropy) solution of CL-DF. We continue the discussion with the applications of CL-DF to the system of non strictly hyperbolic conservation laws, where we propose an efficient numerical method which overcomes certain major difficulties in the existing methods. With the stability analysis, this method is utilized to discretize a system of equations which models the multicomponent polymer flooding problem of enhanced oil recovery process. In the latter half, together with stability analysis we discuss about a mixed high order discretization of a coupled flow transport equations modeling two-phase flow. We continue this section with the description of a proposed high order approximate Lax-Wendroff discontinuous Galerkin method for general hyperbolic system of conservation laws, where we treat the system of Euler equations as an example. We wind up all our discussion with certain future work in this direction.

Date and Time : 23-03-2017 15:00

Venue : Seminar Hall, 219 @ CET

Speaker : Sudarshan Kumar K, University of Concepcion, Chile