Higher Order Accurate Bounds Preserving Time-Implicit Discretizations for the Chemically Reactive Euler Equations (Communications in Computational Physics, 2025)
We construct higher order accurate bounds preserving time-implicit Discontinuous Galerkin (DG) discretizations for the reactive Euler equations modellingmultispecies and multireaction chemically reactive flows. In numerical discretizationsof chemically reactive flows, the time step can be significantly limited because of thelarge difference between the fluid dynamics time scales and the reaction time scales. Inaddition, the density and pressure should be nonnegative and the mass fractions between zero and one, which imposes constraints on the numerical solution that must besatisfied to obtain physically reliable solutions. We address these issues using the following steps. Firstly, we develop the Karush-Kuhn-Tucker (KKT) limiter for the chemically reactive Euler equations, which imposes bounds on the numerical solution usingLagrange multipliers, and solve the resulting KKT mixed complementarity problemusing a semi-smooth Newton method. The disparity in time scales is addressed using a fractional step method, separating the convection and reaction steps, and the useof higher order accurate Diagonally Implicit Runge-Kutta (DIRK) methods. Finally,Harten’s subcell resolution technique is used to deal with stiff source terms in chemically reactive flows. Numerical results are shown to demonstrate that the boundspreserving KKT-DIRK-DG discretizations are higher order accurate for smooth solutions and able to capture complicated stiff multispecies and multireaction flows withdiscontinuities.