A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consis...A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.展开更多
In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially ...In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially non-oscillatory(WENO-JS)scheme[8]and its variations[2,7],and the monotonicity preserving(MP)scheme[16],for solving the Euler equations.MP is found to be more effective than the three WENO variations studied.AUSM+-UP is also shown to be free of the so-called“carbuncle”phenomenon with the high-order interpolation.The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables,even though they require additional matrix-vector operations.Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison.In addition,four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy.Finally,a measure for quantifying the efficiency of obtaining high order solutions is proposed;the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.展开更多
基金Supported by National Nature Science Foundation of China(No.61070096)the Natural Science Foundation of Shandong Province(No.ZR2012FL05,No.2015ZRE27056)
文摘A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.
基金supported by the Subsonic Fixed Wing and Supersonics Projects under the NASA’s Fundamental Aeronautics Program,Aeronautics Mission Directorate.We also thank H.T.Huynh of NASA Glenn Research Center for his help with the MP method。
文摘In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially non-oscillatory(WENO-JS)scheme[8]and its variations[2,7],and the monotonicity preserving(MP)scheme[16],for solving the Euler equations.MP is found to be more effective than the three WENO variations studied.AUSM+-UP is also shown to be free of the so-called“carbuncle”phenomenon with the high-order interpolation.The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables,even though they require additional matrix-vector operations.Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison.In addition,four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy.Finally,a measure for quantifying the efficiency of obtaining high order solutions is proposed;the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.
