The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. An invariant region of the resulting Euler system is identified and the convexity property of this region is justified by using only very minimal thermodynamical assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter can be constructed for use in high order finite-volume type schemes to solve the compressible Euler equations with a general constitutive relation.
翻译:研究采用一般状态等式的压缩尤勒方程式的解决方案的状态空间。允许任意的状态方程式,但只受热动力学的物理要求限制。由此而形成的尤勒系统的一个变化无常的区域被确定出来,通过仅使用极小的热动力学假设,可以证明这一地区的静电特性是合理的。最后,我们展示如何建造一个不变化区域保留限值(IRP)限制器,用于高顺序的有限量型计划,以解决具有一般组成关系的可压缩尤勒方程式。