标题： 一个高效且能量稳定的分散多相流IMEX分裂格式 显示英文标题

标题： An efficient and energy-stable IMEX splitting scheme for dispersed multiphase flows

摘要： 采用体积平均化的Navier–Stokes方程在各种应用中被用来模拟具有两个或多个相互渗透相的系统。每种流体遵循其自身的动量和质量方程，各相通常通过拖曳力和共享压力耦合在一起。因此，整体求解器可能非常昂贵且难以实现。另一方面，设计稳健的分裂方案需要使压力和拖曳力显式化，而不牺牲时间稳定性。在此背景下，我们基于平均速度场的不可压缩性推导了一种新的第一阶压力校正方法，并结合了拖曳力的显式处理。此外，对流项使用外推速度线性化，而粘性项则半隐式处理。这为我们提供了一种隐式-显式（IMEX）方法，不仅由于其无条件的能量稳定性而非常稳健，而且因为它不需要任何形式的固定点迭代。每个时间步仅涉及线性的标量输运方程和一个Poisson问题作为构建块，从而提供了效率和简洁性。我们严格证明了无时间步长限制的时间稳定性，理论通过两相数值例子得到了验证。 显示英文摘要

摘要： Volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled via drag forces and a shared pressure. Monolithic solvers can therefore be very expensive and difficult to implement. On the other hand, designing robust splitting schemes requires making both pressure and drag forces explicit without sacrificing temporal stability. In this context, we derive a new first-order pressure-correction method based on the incompressibility of the mean velocity field, combined with an explicit treatment of the drag forces. Furthermore, the convective terms are linearised using extrapolated velocities, while the viscous terms are treated semi-implicitly. This gives us an implicit-explicit (IMEX) method that is very robust not only due to its unconditional energy stability, but also because it does not require any type of fixed-point iterations. Each time step involves only linear, scalar transport equations and a single Poisson problem as building blocks, thereby offering both efficiency and simplicity. We rigorously prove temporal stability without any time-step size restrictions, and the theory is confirmed through two-phase numerical examples.