Chemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system may contain stiff source terms. (2) The transition points near the shocks may trigger the stiff source leading to spurious shock speed. (3) Physically, the density, internal energy are positive, and the mass fractions are between 0 and 1. In this talk, we discuss recent advances of high-order discontinuous Galerkin and finite difference methods for chemically reacting flows. We introduce the bound-preserving techniques for spatial derivatives. Several effective time integrations are developed. Finally, to suppress oscillations, we discuss the oscillation-free algorithm.
In 2005, Professor Yang Yang joined the Department of Modern Mechanics at University of Science and Technology of China. One year later, he transferred to the Math Department and studied pure math, especially analysis. After receiving his Bachelor's degree of Mathematics in 2009, he started his graduate studies at Brown University and worked with Professor Chi-Wang Shu on Numerical Analysis.
His work mainly focused on high order numerical methods for time-dependent problems. It includes three parts: Approximations to delta-functions, Superconvergence of discontinuous Galerkin methods and Numerical cosmology. After obtaining his Ph.D. degree in 2013, he joined the Department of Mathematical Sciences at Michigan Technological University. In 2017, he was promoted to associate professor with tenure. In 2021, he was promoted to professor with tenure.