基于精确Riemann求解器的明满流过渡过程模拟

Preissmann窄缝法模拟明满流过渡过程方法简单,但存在明显的非物理振荡,抑制非物理振荡是该方法应用的关键。基于Godunov格式和精确Riemann求解器对明满流过渡过程进行模拟,针对Riemann问题代数恒等式在明满流交界处不光滑问题,提出了三阶收敛方法与二分法结合的迭代求解方法,保证迭代收敛至真实解;针对由于变量空间重构方法不能准确表达变量在空间中真实物理状态而导致的非物理振荡,提出了基于精确Riemann解的变量空间重构方法,准确表达激波间断在单元内的空间分布状态,从机理上抑制了非物理振荡。实例研究表明,数值计算结果与解析解或实测值吻合良好,研究成果为明满流过渡过程的高精度数值模拟提供了新的方法。

基于精确Riemann求解器的复杂明渠水流运动模拟

断面几何形状复杂条件下一维明渠水流运动高精度模拟面临较大困难。该文以守恒形式圣维南方程作为控制方程,提出基于动量方程的变量空间重构方法,在动量方程中增加因断面宽度变化而产生的侧压力项,适用于混合流及断面几何形状复杂等条件下变量空间的精确重构。数值计算方面,基于Godunov格式,采用精确Riemann求解器对复杂明渠水流运动进行高精度模拟。实例研究表明,数值计算结果与解析解或实测值吻合良好,算法具备和谐、稳健和高精度等特点,特别适用于泄水闸泄流等复杂明渠水流运动数值模拟,具有较高的实用价值。

A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase flows.The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface,the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side.An exact Riemann solver,between the Euler equation and the six-equation model with highly nonlinear Mie-Gr¨uneisen equations of state,is developed to predict the interfacial states and compute the phase interface flux.Several numerical examples,including shock tube problems,cavitation problems,air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.