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A LINEARLY-FITTED CONSERVATIVE (DISSIPATIVE) SCHEME FOR EFFICIENTLY SOLVING CONSERVATIVE (DISSIPATIVE) NONLINEAR WAVE PDES 被引量:1
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作者 Kai Liu XinyuanWu Wei Shi 《Journal of Computational Mathematics》 SCIE CSCD 2017年第6期780-800,共21页
The extended discrete gradient method is an extension of traditional discrete gradient method, which is specially designed to solve oscillatory Hamiltonian systems efficiently while preserving their energy exactly. In... The extended discrete gradient method is an extension of traditional discrete gradient method, which is specially designed to solve oscillatory Hamiltonian systems efficiently while preserving their energy exactly. In this paper, based on the extended discrete gradient method, we present an efficient approach to devising novel schemes for numerically solving conservative (dissipative) nonlinear wave partial differential equations. The new scheme can preserve the energy exactly for conservative wave equations. With a minor remedy to the extended discrete gradient method, the new scheme is applicable to dissipative wave equations. Moreover, it can preserve the dissipation structure for the dissipative wave equation as well. Another important property of the new scheme is that it is linearly-fitted, which guarantees much fast convergence for the fixed-point iteration which is required by an energy-preserving integrator. The efficiency of the new scheme is demonstrated by some numerical examples. 展开更多
关键词 conservative (dissipative wave pdes Structure-preserving algorithm Linearly-fitted Average Vector Field formula Sine-Gordon equation.
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Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth 被引量:35
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作者 Hong Guangwen Professor, Research Institute of Coastal and Ocean Engineering, Hohai University, 1 Xikang Road, Nanjing 210024 《China Ocean Engineering》 SCIE EI 1996年第4期433-454,共22页
Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory an... Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given. 展开更多
关键词 refraction-diffraction dissipATION wave action conservation eikonal equation time-dependent ild slope equation orthogonal curvilinear coordinates
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Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography 被引量:5
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作者 Hong, GW Feng, WB +1 位作者 Xia, QY Pan, SH 《China Ocean Engineering》 SCIE EI 1997年第4期373-386,共14页
A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the di... A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice. 展开更多
关键词 refraction-diffraction of waves on current wave number conservation wave action conservation Eikonal equation time dependent mild slope equation on current energy dissipation
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近岸非平整海底上耗散动力系统的广义波作用量守恒方程 被引量:2
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作者 黄虎 《力学学报》 EI CSCD 北大核心 2003年第4期461-464,共4页
为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制,着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响,由基于黏性流体Navier-Stokes方程的平均流方程,建立了近岸耗... 为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制,着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响,由基于黏性流体Navier-Stokes方程的平均流方程,建立了近岸耗散动力系统的广义波作用量守恒方程,从中提出垂向速度波作用量和耗散波作用量这两种新概念,使得它们和经典的波作用量相互间达成了一种互补、协调而又主次分明的更为广泛的守恒形式。从而把波作用量这一经典概念从理想的平均流守恒系统引申到实际的平均流耗散系统(即广义守恒系统)中去,为解释沿岸过程和应用于近海、海岸工程提供了一个理论基础。 展开更多
关键词 耗散动力系统 广义波作用量守恒 平均流方程 非平整海底 NAVIER-STOKES方程 近海岸
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耗散SLRW方程的一个新的守恒差分逼近 被引量:2
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作者 林雪梅 胡劲松 刘倩 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2014年第1期49-53,共5页
利用Lax格式的离散思想,引入加权系数,对耗散对称正则长波方程的初边值问题提出了一个带有加权系数a的3层线性差分格式,格式合理地模拟了问题的2个守恒律,得到了差分解的先验估计,分析了该格式的二阶收敛性与稳定性.数值实验表明,该方... 利用Lax格式的离散思想,引入加权系数,对耗散对称正则长波方程的初边值问题提出了一个带有加权系数a的3层线性差分格式,格式合理地模拟了问题的2个守恒律,得到了差分解的先验估计,分析了该格式的二阶收敛性与稳定性.数值实验表明,该方法是可信的,且适当调整加权系数,可以大幅提高计算精度. 展开更多
关键词 耗散对称正则长波方程 差分格式 守恒 收敛性 稳定性
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(2+1)维耗散长水波方程组的精确解和守恒律
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作者 杨飞 刘希强 《河北师范大学学报(自然科学版)》 CAS 2018年第2期93-99,共7页
利用李群方法得到了(2+1)维耗散长水波方程组的对称,获得了相应的约化方程,并求出其精确解.所得结果推广了已有文献中该方程的相关结果.利用得到的对称求出了(2+1)维耗散长水波方程组的守恒律.
关键词 对称 约化 (2+1)维耗散长水波方程组 精确解 守恒律
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A ESTIMATE OF THE RATE OF ENTROPY DISSIPATION OF HIGH RESOLUTION MUSCL TYPE GODUNOV SCHEMES 被引量:1
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作者 Tang, HZ Zhao, N 《Journal of Computational Mathematics》 SCIE CSCD 1999年第4期369-378,共10页
In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-L... In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vincity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a 'sharp' condition on limiter function in order to keep its entropy dissipation and its convergence. 展开更多
关键词 hyperbolic conservation laws MUSCL type Godunov schemes entropy dissipation shock wave rarefaction wave
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耗散SRLW方程的一个非线性守恒加权差分算法 被引量:1
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作者 晏力 胡劲松 +1 位作者 王正华 林雪梅 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2013年第5期917-922,共6页
我们对具有耗散项的对称正则长波方程的初边值问题进行了数值研究,提出了一个带有加权系数θ的两层Crank-Nicolson差分格式,格式合理地模拟了问题本身的两个守恒量.在差分解的先验估计基础上我们用能量方法分析了该格式的二阶收敛性与... 我们对具有耗散项的对称正则长波方程的初边值问题进行了数值研究,提出了一个带有加权系数θ的两层Crank-Nicolson差分格式,格式合理地模拟了问题本身的两个守恒量.在差分解的先验估计基础上我们用能量方法分析了该格式的二阶收敛性与无条件稳定性.数值试验表明该方法是可信的,且适当调整加权系数θ可以大幅提高格式的计算精度. 展开更多
关键词 耗散 对称正则长波方程 差分格式 守恒 收敛性 稳定性
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带阻尼项的广义SRLW方程的一个守恒差分格式 被引量:1
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作者 刘倩 胡劲松 林雪梅 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2014年第2期219-223,共5页
本文对带有阻尼项和耗散项的广义对称正则长波方程的初边值问题进行了数值研究,提出了一个两层非线性有限差分格式,该格式合理地模拟了问题本身的一个守恒性质,讨论了差分解的先验估计,并用能量方法分析了该格式的二阶收敛性与无条件稳... 本文对带有阻尼项和耗散项的广义对称正则长波方程的初边值问题进行了数值研究,提出了一个两层非线性有限差分格式,该格式合理地模拟了问题本身的一个守恒性质,讨论了差分解的先验估计,并用能量方法分析了该格式的二阶收敛性与无条件稳定性,最后利用数值算例验证了格式的可靠性. 展开更多
关键词 阻尼耗散 广义对称正则长波方程 差分格式 守恒 收敛性 稳定性
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