用四阶Runge-Kuta法和TVD格式求解两维跨超音流场

COMPUTATION OF 2-D TRANSONIC AND SUPERSONIC FLOW FIELDS USING TVD SCHEME AND FOUR-STAGE RUNGE-KUTTA TECHNIQUE

利用坐标转换给出两维任意曲线坐标系下雅可比矩阵特征值、特征向量及Ｈａｒｔｅｎ型ＴＶＤ格式的详细表达式，并结合四阶Ｒｕｎｇｅ－Ｋｕｔａ法发展了一种新的、有效的求解超音、跨音流场的算法。数值计算表明，本文的方法可有效地求解跨音流场。

Harten′s TVD scheme is extented to 2-D general curvilinear coordinates by local rotation matrix translation.A new fully explicit solving method based on Four-Stage Runge-Kutta technique is developed to predict 2-D supersonic and transonic flow field.Comparison between computation and experiment is presented for both supersonic and transonic flow.The numerical results show that this scheme is not only convenient to solve the supersonic flow,but also capable of predicting the transonic flow.