关于为任意状态方程构造高阶和精确压力平衡方案的研究
On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State
AI总结：
本文提出两种通用方法，用于为任意状态方程构造高阶精确压力平衡方案，有效减少虚假压力振荡。
摘要：
典型的完全保守的欧拉可压缩单组分或多组分流体方程的离散化，由于压力、密度和内能之间热力学关系的非线性，表现出虚假的压力振荡。本文提出了一个完全保守、压力平衡保持的方法以及一个高阶、完全保守、近似压力平衡保持的方法。这两种方法都具有通用性，能够处理任意的状态方程和任意数量的组分。与现有方法不同，我们没有引入非保守更新、超指定方程或为特定状态方程设计。所提出的方法在由三种状态方程（理想气体、刚性气体和范德瓦尔方程）支配的无粘光滑界面传播问题中得到验证，显示出与现有方案相比压力振荡的量级减少。
英文摘要：
Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic relation between pressure, density, and internal energy. A fully conservative, pressure-equilibrium preserving method and a high-order, fully conservative, approximate pressure-equilibrium preserving method are presented. Both methods are general and can handle an arbitrary equation of state and arbitrary number of species. Unlike existing approaches to discretize the multi-component Euler equations, we do not introduce non conservative updates, overspecified equations, or design for a specific equation of state. The proposed methods are demonstrated on inviscid smooth interface advection problems governed by three equations of state: ideal-gas, stiffened-gas, and van der Waals where we show orders of magnitude reductions in spurious pressure oscillations compared to existing schemes.
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。
