可压缩多介质流体的真正多维高保真算法

Compressible multi-fluid flows can be found in a variety of science and engineering problems, such as national economy and defense technology, and they are characterized by the interaction of shock waves and material interfaces in multidimensional space. Due to the difficulty of theoretical and experimental research, numerical simulation is playing a more and more important role, and more attention are.paid on the fidelity of numerical methods. Development of numerically accurate and computationally efficient algorithms for multi-material flow simulations remains one of the unresolved issues in computational fluid dynamics. Dimensional splitting for multidimensional problems and flag variable for multi-fluid interfaces are two frequently used techniques for multidimensional flows with large deformations. However,.fidelity of simulation is reasonable based on such techniques. Genuine multidimensional algorithms and suitable modeling based on physics will be the key points of simulation for multi-fluid flows with large deformation. The interaction between nonlinear waves and material interface will be investigated based on the studies of genuine multidimensional Riemann solver and large deformation interface modeling, and Genuine multidimensional oscillation-free methods with high fidelity will be constructed to overcome the difficulty of nonlinear numerical instability and nonphysical numerical oscillations. Overall, the research work is of creativity and value of application and is hopeful to provide some algorithm and code facilities for the practical engineering problems.

可压缩多介质流体具有多维、多介质、强压缩间断等特征，由于理论分析和实验研究的困难，数值模拟是研究这类问题的主要手段，然而由于缺乏可靠的理论分析和实验数据，而目前数值模拟方法的置信度又缺乏可靠验证，多介质大变形问题是一个长期研究而又进展不大的泥潭课题。发展真正多维的高保真算法，将是多介质大变形问题研究的一个关键所在。课题组将从真正多维的Riemann解子器入手，结合多介质流体的具体模型，认知多维非线性波和物质界面的物理机理，凝练实际应用中的多介质模型，构造能够克服非线性波数值不稳定性和界面数值震荡的真正多维的高保真算法。本项目研制能够有效模拟多介质大变形流动的高保真方法和程序，将能为实际工程问题提供有力的方法和程序支撑，有创新性和较高的应用价值。

可压缩多介质流体具有多维、多介质、强压缩间断等特征，由于理论分析和实验研究的困难，数值模拟是研究这类问题的主要手段，然而由于缺乏可靠的理论分析和实验数据，而目前数值模拟方法的置信度又缺乏可靠验证，多介质大变形问题是一个长期研究而又进展不大的泥潭课题。发展真正多维的高保真算法，将是多介质大变形问题研究的一个关键所在。课题组将流场的切向速度变化加入到数值流通量中去，真正实现非线性的真正多维黎曼黎曼解法器；并在此基础上发展了时空高精度的数值格式；引入耗散理论，分析了守恒性格式的数值稳定性；系统地探讨了采用高精度有限差分方法模拟多介质问题时存在的问题和解决的思路；构造高精度、低耗散的单调保持格式；研究了适合具有复杂状态方程形式的多介质Roe平均方法。本项目研制的算法能够有效模拟多介质大变形流动，能为实际工程问题提供有力的方法和程序支撑，有创新性和较高的应用价值。

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