The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to ...The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed,and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust.More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.展开更多
In this paper, the cell face velocities in the discretization of the continu- ity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum...In this paper, the cell face velocities in the discretization of the continu- ity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations. Their performances are compared. When the linear interpolation is used to calculate the coefficients, the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51736008 and 51276092)
文摘The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed,and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust.More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.
基金Project supported by the National Natural Science Foundation of China (Nos. 51176204 and 51134006)
文摘In this paper, the cell face velocities in the discretization of the continu- ity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations. Their performances are compared. When the linear interpolation is used to calculate the coefficients, the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution.
