This paper develops a low-diffusion robust flux splitting scheme termed TVAP to achieve the simulation of wide-ranging Mach number flows.Based on Toro-Vazquez splitting approach,the new scheme splits inviscid flux int...This paper develops a low-diffusion robust flux splitting scheme termed TVAP to achieve the simulation of wide-ranging Mach number flows.Based on Toro-Vazquez splitting approach,the new scheme splits inviscid flux into convective system and pressure system.This method introduces Mach number splitting function and numerical sound speed to evaluate advection system.Meanwhile,pressure diffusion term,pressure momentum flux,interface pressure and interface velocity are constructed to measure pressure system.Then,typical test problems are utilized to systematically assess the robustness and accuracy of the resulting scheme.Matrix stability analysis and a series of numerical cases,such as double shear-layer problem and hypersonic viscous flow over blunt cone,demonstrate that TVAP scheme achieves excellent low diffusion,shock stability,contact discontinuity and low-speed resolution,and is potentially a good candidate for wide-ranging Mach number flows.展开更多
The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are d...The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras(SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests(Qo Is). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori(MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.展开更多
基金supported by the Space Science and Technology Fund Project of China(No.2020-HT-XG-14)。
文摘This paper develops a low-diffusion robust flux splitting scheme termed TVAP to achieve the simulation of wide-ranging Mach number flows.Based on Toro-Vazquez splitting approach,the new scheme splits inviscid flux into convective system and pressure system.This method introduces Mach number splitting function and numerical sound speed to evaluate advection system.Meanwhile,pressure diffusion term,pressure momentum flux,interface pressure and interface velocity are constructed to measure pressure system.Then,typical test problems are utilized to systematically assess the robustness and accuracy of the resulting scheme.Matrix stability analysis and a series of numerical cases,such as double shear-layer problem and hypersonic viscous flow over blunt cone,demonstrate that TVAP scheme achieves excellent low diffusion,shock stability,contact discontinuity and low-speed resolution,and is potentially a good candidate for wide-ranging Mach number flows.
基金supported by the National Numerical Windtunnel Project,China(No.NNW2019ZT1-A03)the National Natural Science Foundation of China(No.11721202)。
文摘The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras(SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests(Qo Is). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori(MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.
