捕捉激波和接触不连续性的新型流体动力学格式及与现有方法的比较研究
Novel Hydrodynamic Schemes Capturing Shocks and Contact Discontinuities and Comparison Study with Existing Methods
AI总结：
提出无需人工参数的 GDISPH 流体动力学格式，通过将 Riemann 求解器整合至 DISPH 中，有效处理激波与接触不连续性，标准测试表明其优于现有方法且不引入额外数值扩散。
摘要：
我们提出了一种名为 Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH) 的新型流体动力学格式，它无需任何手动调节的参数即可精确处理激波和接触不连续性。这与标准形式的 smoothed particle hydrodynamics (SSPH) 形成对比，后者需要人工粘性项的参数来处理激波，并且由于非物理排斥力难以精确处理接触不连续性，从而产生表面张力，破坏压力平衡并抑制流体不稳定性。虽然 Godunov SPH (GSPH) 可以通过使用 Riemann 求解器的解来在无参数情况下处理激波，但它仍无法完全处理接触不连续性。Density-Independent Smoothed Particle Hydrodynamics (DISPH) 是为了比 SSPH 更有效地处理接触不连续性而提出的几种格式之一，在涉及强激波和接触不连续性的测试中表现出优越的性能。然而，DISPH 仍然需要人工粘性项。我们以多种方式将 Riemann 求解器整合到 DISPH 中，产生了若干 GDISPH 变体。一维 Riemann 问题、压力平衡、Sedov-Taylor 和 Kelvin-Helmholtz 测试等标准测试的结果对 GDISPH Case 1 和 GDISPH Case 2 以及 DISPH 有利。我们得出结论，GDISPH Case 1 相比 GDISPH Case 2 具有优势，能够有效处理激波和接触不连续性，而无需特定参数或引入任何额外的数值扩散。
英文摘要：
We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast to the standard formulation of smoothed particle hydrodynamics (SSPH), which requires the parameters for an artificial viscosity term to handle the shocks and struggles to accurately handle the contact discontinuities due to unphysical repulsive forces, resulting in surface tension that disrupts pressure equilibrium and suppresses fluid instabilities. While Godunov SPH (GSPH) can handle the shocks without the parameters by using solutions from a Riemann solver, it still cannot fully handle the contact discontinuities. Density-Independent Smoothed Particle Hydrodynamics (DISPH), one of several schemes proposed to handle contact discontinuities more effectively than SSPH, demonstrates superior performance in our tests involving strong shocks and contact discontinuities. However, DISPH still requires the artificial viscosity term. We integrate the Riemann solver into DISPH in several ways, yielding some patterns of GDISPH. The results of standard tests such as the one-dimensional Riemann problem, pressure equilibrium, Sedov-Taylor, and Kelvin-Helmholtz tests are favourable to GDISPH Case 1 and GDISPH Case 2, as well as DISPH. We conclude that GDISPH Case 1 has an advantage over GDISPH Case 2, effectively handling shocks and contact discontinuities without the need for specific parameters or introducing any additional numerical diffusion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
