We present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

我们提出了一个 SPH 公式，它具有几个新特性，旨在更好地模拟不同材料的完全可压缩相互作用。我们开发了一种新方法来模拟行星大气中小天体的大气进入和分裂。该公式使用具有线性校正内核梯度的流体动力学守恒定律的基于单位的密度能量离散化。为了解释可压缩性的变化，我们使用 HLLC 近似黎曼求解器来调整材料界面处的速度梯度。为了处理大的横向速度不连续性，我们引入了一个简单的滑动界面模型，该模型限制了材料界面处的人工粘度。通过速度梯度可选地应用扩散，与其他更直接的扩散方案相比，这允许密度和比热能以更符合热力学第一定律的方式演变。我们还介绍了一种用于平滑特定热能场的材料局部二阶人工传导方案。通过将损伤前沿视为材料界面，材料损伤非常适合该框架。该方法已在代码 Spheral++ 中作为求解器 FSISPH 实现，并可在 github 上公开获得。我们在一些经典的冲击、混合和多材料问题上测试了我们的新求解器。我们概述的组件可以显着提高 SPH 对尖锐接触不连续问题的准确性。