Final Report Summary - SPARCCLE (STRUCTURE PRESERVING APPROXIMATIONS FOR ROBUST COMPUTATION OF CONSERVATION LAWS AND RELATED EQUATIONS) The SPARCCLE project focussed on the design, analysis and efficient implementation on state of the art massively parallel high performance computing architectures, of numerical algorithms for simulating solutions of systems of conservation laws and related equations. These nonlinear partial differential equations (PDEs) arise in a wide variety of contexts in fluid and plasma dynamics and their solutions are characterized by complex structures such as shocks, instabilities, turbulence etc. The project was successful in designing finite difference, finite volume and discontinuous Galerkin finite element methods that were entropy stable i.e consistent with discrete versions of the second law of thermodynamics. Moreover, these very high-order algorithms preserved interesting classes of equilibrium states and were able to approximate small scale dependent shock waves of arbitrary strength. A key focus of the project was on the computation of entropy measure-valued solutions for systems of conservation laws. This solution framework arises in the context of quantifying uncertainty in these PDEs and we provided efficient algorithms to compute these solutions. The algorithms were shown to scale efficiently on state of the art HPC hardware platforms and were applied to solve realistic problems in variety of applications such as in astrophysics, geophysics and climate science.
