论文标题
范德华气体中弱非线性双曲波的分析和数值研究
Analytical and numerical study of weakly nonlinear hyperbolic waves in a van der Waals gas
论文作者
论文摘要
在本文中，我们表征了具有真实气体背景的气体动力学中弱非线性双曲波的共振相互作用。一种渐近方法用于研究由气体动力学的Euler方程控制的波之间的相互作用，并补充了范德华的状态方程。进化方程是由汉堡类型的非线性项和带有已知核的卷积项组成的深度分化方程。在分析和数值上研究了一个用于各种范德华参数值的行驶波解决方案的一个参数家族。研究了范德华参数对行驶波解决性质的影响的影响。关于任意初始数据演变的数值实验是使用分数步骤算法进行的，描述了IntegroDiffrential方程中卷积项的行为。所有时间解决方案的非破坏的存在得到了数值的证实。
In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of gas dynamics, supplemented by a van der Waal equation of state; the evolution equation is an integro-differential equation composed of a Burgers type nonlinear term and a convolution term with a known kernel. A one parameter family of traveling wave solutions for various values of van der Waals parameter is studied analytically and numerically. Effect of the influence of van der Waals parameter on the properties of traveling waves solution is investigated. Numerical experiments on the evolution of arbitrary initial data are performed using fractional step algorithm, describing the behavior of convolution term in the integrodiffrential equation. The existence of non breaking for all time solutions is substantiated numerically.
