转动坐标系中三维跨声速欧拉流的有限体积 TVD格式

在非惯性转动坐标系中,本文采用贴体网格、有限体积法离散和修正数值通量技术,将Harten的一维TVD格式推广到三维。由于转动使方程出现源项,文中通过对源项的巧妙处理,使修改后的格式能用于非齐次双曲守恒律方程组高分辨率的数值计算。为了加速解的收敛,提高显式时间推进的CFL数,本文采用隐式残值光顺技术。三维跨声速带非齐次源项欧拉方程的典型算例表明:捕捉的激波分辨率较高;激波前后没有发现大的数值波动和伪振荡现象;所得的跨声速流场解与实验较接近。

Finite Volume-TVD Scheme for 3-D Euler Transonic Flows Computations in Rotating Curvilinear Coordinates

An efficient algorithm that exploits the properties of both total variation diminishing(TVD) schemes developed by Harten and Runge-Kutta ones dnveloped by Jameson is presented in this paper. In the algorithm, TVD is implemented in the framework of an explicit finite volume approach. The discretized flux at an arbitrary computational cell interface is evaluated by Harten's modified numerical flux. Time integration of the system of ordinary differential e-quations, obtained after spatial discretization, is performed by a Runge-Kutta algorithm and implicit residuals averaging technique in accelerating convergence. The goal of this work is to extend one-dimensional Harten' s scheme to three dimensional nonlinear hyperbolic conservation laws with source (i, e. , nonhomogeneous hyperbolic conservation laws). The new algorithm has been used to compute 3-D Euler transonic or supersonic flows in rotating frame of reference.Numerical test has been selected the 3-D transonic flow field within an axial-flow single-stage compressor rotor tested by DFVLR. The rotating frame has been selected a body-fitted coordinate system rotating with the blade row. Comparisons between the computed flow field and the experimental data have been made. It is clear that the agreement of prediction with experiment is good. Numerical results show that this algorithm can capture the shock in 1-3 grid points. It indicated that the algorithm is quite robust and can generate good shock resolution.