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 87 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 81 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如何计算跨越材料界面的平流通量，这些界面将热力学状态与关系截然不同的区域分隔开。对此，一种常见思路是局部构造双材料黎曼问题，并将其精确解用于通量计算。然而，对于一般状态方程，求解黎曼问题的精确解需要嵌套循环，计算代价高昂。当模拟过程中需要构造大量黎曼问题时，计算成本往往变得难以承受。本文旨在加速双材料黎曼问题的求解，无需引入近似或离线预计算。基本思路是利用黎曼问题方程的一些特殊性质，并尽可能复用先前的解。基于此思路，我们提出了四种加速方法：(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) 在线构建R树以生成初始猜测。通过水下爆炸、激光诱导空化和超高速撞击等四个算例评估了这些加速方法的性能。这些算例表现出强激波、大界面变形、多界面（>2个）接触以及气体与凝聚态物质的相互作用。在这些具有挑战性的情况下，双材料黎曼问题的求解速度提升了37至87倍。因此，平流通量计算的总成本（包括材料界面处的精确黎曼问题求解和整个计算域内的数值通量计算）加速了18至81倍。