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Center for Nonlinear Studies |
Theoretical studies and numerical experiments suggest that unstructured high-order methods (such as discontinuous Galerkin methods and spectral difference methods) can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it is the case that existing unstructured high-order schemes are less robust and more complex to implement than their simpler low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of unstructured high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is almost ubiquitous). In this seminar I will discuss recent efforts to develop simple, efficient and robust unstructured high-order methods based on the so called flux reconstruction (FR) approach. Particular attention will focus on a new range of energy-stable FR schemes [1], from which various existing high-order methods can be recovered as special cases. The theory behind these new methods will be detailed, along with issues of practical implementation for both multi-CPU and multi-GPU architectures. Finally, examples of how unstructured high-order schemes can be applied to solve biologically inspired flow problems will be presented.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400