We study the quasi-random choice method （QRCM） for the Liouville equation of ge- ometrical optics with discontinuous locM wave speed. This equation arises in the phase space computation of high frequency waves throu...We study the quasi-random choice method （QRCM） for the Liouville equation of ge- ometrical optics with discontinuous locM wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discon- tinuities, and measure-valued solutions. The so-called QRCM is a random choice method based on quasi-random sampling （a deterministic alternative to random sampling）. The method not only is viscosity-free but also provides faster convergence rate. Therefore, it is appealing for the prob!em under study which is indeed a Hamiltonian flow. Our analy- sis and computational results show that the QRCM 1） is almost first-order accurate even with the aforementioned discontinuities; 2） gives sharp resolutions for all discontinuities encountered in the problem; and 3） for measure-valued solutions, does not need the level set decomposition for finite difference/volume methods with numerical viscosities.展开更多
利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发...利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.展开更多
An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque,and an exact Riemann solver is used.A multiple wave approximation approach was...An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque,and an exact Riemann solver is used.A multiple wave approximation approach was suggested for eliminating the discontinuities found in the rarefaction fans of dam-breaking flows.In addition,we use the random choice method to reduce non-physical oscillations.Applications demonstrate that the algorithm proposed in this paper can considerably increase the CFL number up to 25when modeling dam-break flows,while retaining satisfactory accuracy and efficiency.This suggests that our algorithm has the potential to be applied to modeling free surface flows.展开更多
文摘We study the quasi-random choice method （QRCM） for the Liouville equation of ge- ometrical optics with discontinuous locM wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discon- tinuities, and measure-valued solutions. The so-called QRCM is a random choice method based on quasi-random sampling （a deterministic alternative to random sampling）. The method not only is viscosity-free but also provides faster convergence rate. Therefore, it is appealing for the prob!em under study which is indeed a Hamiltonian flow. Our analy- sis and computational results show that the QRCM 1） is almost first-order accurate even with the aforementioned discontinuities; 2） gives sharp resolutions for all discontinuities encountered in the problem; and 3） for measure-valued solutions, does not need the level set decomposition for finite difference/volume methods with numerical viscosities.
文摘利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.
基金supported by the National Basic Research Program of China (2011CB403304,2011CB409901)the National Natural Science Foundation of China (51039004,51109009)
文摘An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque,and an exact Riemann solver is used.A multiple wave approximation approach was suggested for eliminating the discontinuities found in the rarefaction fans of dam-breaking flows.In addition,we use the random choice method to reduce non-physical oscillations.Applications demonstrate that the algorithm proposed in this paper can considerably increase the CFL number up to 25when modeling dam-break flows,while retaining satisfactory accuracy and efficiency.This suggests that our algorithm has the potential to be applied to modeling free surface flows.
