CISM-ECCOMAS International Summer School on "Efficient High-order Discretizations for Computational Fluid Dynamics"
- Sonia Fernández-Méndez (Universitat Politècnica de Catalunya, Barcelona, Spain)
6 lectures on: Hybridizable Discontinuous Galerkin (HDG) methods for the Laplace equation: implementation, revision of a Matlab code, convergence and superconvergence, efficiency comparison vs continuous FEM. HDG formulation for incompressible flow problems: implementation, Matlab code, efficiency and stability comparison vs continuous FEM.
- Gregor Gassner (Köln University, Germany)
6 lectures on: Split-form discontinuous Galerkin methods for compressible Fluid Dynamics, DG and summation-by-parts, discrete stability and de-aliasing, high order DG and explicit turbulence modeling.
- Martin Kronbichler (Technical University of Munich, Germany)
7 lectures on: Introduction to discontinuous Galerkin methods for scalar transport equations, sum factorization for evaluation of integrals in context of explicit time integration, efficient solution of linear systems with fast operator evaluation and its limitations. High-performance computing aspects in DG: parallel scalability and fast absolute performance on the next-generation exascale computers.
- Rainald Lohner (George Mason University, Fairfax, VA, USA)
4 lectures on: The tradeoff of high versus low order methods: What accuracy is relevant in an engineering application? What is the speed/accuracy ratio of high order methods? What happens to high order methods in applications where monotonicity is important? Are high order methods relevant for applications where butterfly effects are present?
- Per-Olof Persson (University of California, Berkeley, USA)
6 lectures on: Practical use of high-order discontinuous Galerkin methods for problems in fluid and solid mechanics: sparse discretizations, efficient preconditioners and iterative solvers, parallel implementations, calculations of sensitivities using fully discrete adjoints. Various methods for generation of appropriate curvilinear meshes. Specialized solvers for multiphysics problems such as fluid-structure interaction.
- Stefano Rebay (University of Brescia, Italy)
6 lectures on: Accurate numerical fluxes for compressible and for incompressible flows: numerical fluxes in finite volume and DG approximations of hyperbolic problems, exact and approximate Riemann solvers, Riemann solvers and high-order accurate DG methods, application to incompressible flows, limitations related to specific problem physics (low mach numbers, low shock speeds, wall overheating, etc.).