Thermodynamic effects of compressible fluid dynamics and application to high resolution schemes of hyperbolic systems
数学专题报告
报告题目(Title)：Thermodynamic effects of compressible fluid dynamics and application to high resolution schemes of hyperbolic systems
报告人(Speaker)：汪玥 (北京应用物理与计算数学研究所)
地点(Place)：教四106
时间(Time)：2023 年 5月 26 日(周五), 10：00—11：00
邀请人(Inviter)：熊金钢
报告摘要
One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical schemes. Unfortunately, the role of entropy, expressing irreversibility, is often neglected even though the entropy inequality, as a conceptual derivative, is verified for some first order schemes. In this talk, the generalized Riemann problem of the Euler system is compared with the Riemann problem to show the differences of the thermodynamical variation. The GRP solver is refined to illustrate how the thermodynamic effects are integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effects in the resolution of strong waves.
As a by-product, a strategy of local stiffened gas approximation with certain thermodynamic compatibility is proposed for computing compressible fluid flows of real materials with the general equation of state. The GRP solver with the new strategy is demonstrated to be efficient and robust through typical numerical examples which display the excellent performance under extreme thermodynamics. Then the GRP solver is combined with the finite volume and DG framework for designing high resolutions schemes and applied for multi-fluid flows.
