Relaxation models for the pressureless gas dynamics (PGD) equations attempt to satisfy the strictly hyperbolic conservation law in order to employ the well-posed approximated Riemann solvers. In this study, a new type of relaxation model is proposed to resolve two shortcomings of the existing relaxation models: the constant propagation speed of sound, and the collapse of delta shock waves in multidimensional problems. The proposed model seeks a strictly hyperbolic system of equations without any special consideration for the proper values of the propagation speed of sound. Numerical tests showed that the proposed model can accurately describe the behavior of the PGD equations, in particular, the occurrence of delta shock waves and vacuum states in a multidimensional problem.

为了采用严格的双曲守恒律，无压力气体动力学（PGD）方程的松弛模型试图采用位置良好的近似Riemann求解器。在这项研究中，提出了一种新型的松弛模型，以解决现有松弛模型的两个缺点：声音的恒定传播速度和多维问题中三角波冲击波的崩溃。所提出的模型寻求严格的双曲方程组，而没有对声音传播速度的适当值进行任何特殊考虑。数值测试表明，该模型可以准确地描述PGD方程的行为，特别是在多维问题中三角波和真空状态的发生。