Discontinuous Galerkin Algorithms for Hyperbolic-Parabolic PDEs

Faculty:  S.V. Raghurama Rao (AE) and Sashikumaar Ganesan (CDS)

Finite Volume Methods (FVM) have been the popular choice for engineering problems modelled by the nonlinear hyperbolic and hyperbolic-parabolic PDEs in the past five decades and have reached high level sophistication in capturing associated discontinuous solutions and other nonlinear waves.  However, achieving higher order accuracy, especially on unstructured meshes, is non-trivial in this framework. Finite Element Methods (FEM), which have been the most preferred algorithms for solving elliptic and parabolic PDEs, have distinct advantages for this task. Combining the strengths of both the approaches led to the development of Discontinuous Galerkin (DG) methods, which are increasingly becoming popular in the last two decades.  We propose to combine the DG framework together with another popular framework for modelling the hyperbolic and hyperbolic-parabolic problems based on the Kinetic or Discrete Velocity Kinetic Systems, which provide semi-linear alternatives to nonlinear conservation laws.  The motivation is to develop novel, efficient and accurate CFD algorithms of interest in several engineering applications.