When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods are assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. In these challenging cases, the solution of bimaterial Riemann problems is accelerated by 37 to 83 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 79 times.

翻译：在求解可压缩多材料流动问题时，一个尚未解决的挑战是计算跨越具有显著不同热力学状态和关系的材料界面的对流通量。对此，一种常用思路是局部构造双材料黎曼问题，并将其精确解应用于通量计算。然而，对于一般状态方程，求解黎曼问题的精确解成本高昂，因为需要嵌套循环。考虑到模拟过程中构造的大量黎曼问题，计算代价往往变得难以承受。本文旨在加速求解双材料黎曼问题，同时避免引入近似或离线预计算任务。基本思路是利用黎曼问题方程的某些特殊性质，并尽可能复用先前解。基于这一思路，本文发展了四种加速方法，包括：(1) 通过稀疏波扇改变积分变量，(2) 存储并重用积分轨迹数据，(3) 步长自适应调整，(4) 动态构建R树以生成初始猜测。利用水下爆炸、激光诱导空化和超高速撞击中的四个算例评估了这些加速方法的性能。这些问题展示了强激波、大界面变形、多界面（>2）接触以及气体与凝聚态物质相互作用。在这些具有挑战性的案例中，双材料黎曼问题的求解速度提升了37至83倍。因此，包含材料界面处精确黎曼问题求解和整个计算域数值通量计算的对流通量总成本，加速了18至79倍。