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.Focusi...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.展开更多
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文摘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.
