Abstract A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).

中文翻译：

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求解无声学时间步长限制的可压缩多相流体流动的半隐式方法

摘要 这里提出了一种新的 3D 多相数值能力，用于在所有马赫数 (M) 下模拟多相流态。新方法是 Chinnaya 等人的有限体积离散方程方法 (DEM) 的半隐式扩展。(2004)，最初使用显式时间步进。该功能还开发为与 DEM 的另一个扩展一起使用，以移动网格，用于 Dunn (2011) 中详述的任意拉格朗日-欧拉 (ALE) 方法。DEM 不是同时求解所有相方程，而是将方程简化为单相黎曼求解系统，其中每个相都有自己的速度和热力学状态。相之间的交换通过解释相相互作用的源项来建模。由于原始多相方案使用显式时间推进方案，它具有由声速决定的时间步长限制，这限制了模型模拟弱可压缩流动的能力，这些流动通常需要在更长的时间段内进行积分。在这里，我们通过实施压力校正步骤来扩展当前的多相公式，以实现隐式计算并消除声学时间步长限制。与显式方法相比，新的半隐式算法允许使用相对较大的时间步长。使用包括弱可压缩流和强冲击波在内的几个示例说明了新的隐式时间步长方法的验证和优点。此处介绍的方案是通用的，可用于需要在各种马赫数下处理多相流能力的各种应用。然而，