Differential Equations Seminar

In the field of computational fluid dynamics (CFD), the persistent pursuit of accurate and efficient simulation of increasingly complex flow problems has pushed traditional low-order (equal to and less than 2) finite volume methods to challenging limits. High-order methods have been gaining popularity due to their great potential to achieve the desired engineering accuracy with lower computational cost compared with low-order methods. This is critical in many engineering fields such as bio-inspired flows, turbulent flows, vortical flows over high-lift configurations, aeroacoustics, and non-hydrostatic atmospheric modeling.

In this talk, challenges in high-order CFD research will be introduced, and the recent effort in the speaker’s group on addressing these challenges will be presented, including novel CFD algorithm development for both compressible and incompressible flows, advanced continuation methods for solving steady flow problems, and effective artificial viscosity design for shock capturing.  Application of the high-order CFD methods in several challenging thermal fluids flow problems, ranging from incompressible to highly compressible regimes, and from steady to highly unsteady regimes, will then be shown. New insights into flow physics underlying some interesting flow phenomena will be discussed.