Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics  

作　　者：Hendrik Ranocha Lisandro Dalcin Matteo Parsani David I.Ketcheson 

机构地区：[1]Applied Mathematics Münster,University of Münster,Munster,Germany [2]Computer Electrical and Mathematical Science and Engineering Division(CEMSE),Extreme Computing Research Center(ECRC),King Abdullah University of Science and Technology(KAUST),Thuwal 23955-6900,Saudi Arabia [3]Computer Electrical and Mathematical Science and Engineering Division(CEMSE),King Abdullah University of Science and Technology(KAUST),Thuwal 23955-6900,Saudi Arabia

出　　处：《Communications on Applied Mathematics and Computation》2022年第4期1191-1228,共38页应用数学与计算数学学报（英文）

基　　金：Open Access funding enabled and organized by Projekt DEAL.

摘　　要：We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.

关 键 词：Explicit Runge-Kutta methods Step size control Compressible Euler equations Compressible Navier-Stokes equations hp-adaptive spatial discretizations 

分 类 号：O35[理学—流体力学]