Robust High-Order Discretizations for Flow Simulations

Jason Hicken, Rensselaer Polytechnic Institute
David Del Rey Fernandez, University of Toronto


High-order discretizations are attractive for simulating fluid flows, because they can achieve the same solution accuracy using many fewer degrees of freedom than lower-order schemes, at least in theory. Yet the use of high-order methods by practitioners is limited, both in industry and academia. This preference for low-order methods has several possible explanations, but we believe robustness is a significant contributor. High-order methods are inherently less dissipative, and this makes them more susceptible to nonlinear instabilities caused by the flow itself or poor quality grids. This motivates the need for more robust high-order methods.

This minisymposium seeks to bring together researchers who are investigating methods to improve the robustness of high-order discretizations. Robust schemes can be constructed by ensuring the discretization conserves global invariants. For example, this approach was pioneered by the incompressible flow community, who developed schemes that discretely conserve kinetic energy. Kinetic-energy conserving methods for compressible flows followed. However, in both cases the discretizations are usually limited to second-order methods on unstructured grids, or moderate-order methods on tensor-product finite-difference grids. Recently, there has been renewed interest in high-order discretizations, both for structured and unstructured grids, that conserve kinetic energy or entropy as a means of achieving robustness.