In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
为了求出对称正则长波(symmetric regularized long wave,SRLW)方程的数值解,构造了一种新的高效紧致有限差分格式.采用经典的Crank-Nicolson(C-N)格式和外推技术对时间方向一阶导数进行离散化,使用四阶Padé方法和逆紧致算子分别...为了求出对称正则长波(symmetric regularized long wave,SRLW)方程的数值解,构造了一种新的高效紧致有限差分格式.采用经典的Crank-Nicolson(C-N)格式和外推技术对时间方向一阶导数进行离散化,使用四阶Padé方法和逆紧致算子分别对空间方向一阶和二阶导数进行离散化,使得构造的格式具有线性、非耦合和紧致的特点,极大地提高了求解效率.此外,还对新格式进行了守恒律、先验估计、稳定性、收敛性分析,证明了其在时间上达到二阶、在空间上达到四阶收敛精度.最后,通过一个数值算例验证了理论的正确性和格式的高效性.展开更多
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
文摘为了求出对称正则长波(symmetric regularized long wave,SRLW)方程的数值解,构造了一种新的高效紧致有限差分格式.采用经典的Crank-Nicolson(C-N)格式和外推技术对时间方向一阶导数进行离散化,使用四阶Padé方法和逆紧致算子分别对空间方向一阶和二阶导数进行离散化,使得构造的格式具有线性、非耦合和紧致的特点,极大地提高了求解效率.此外,还对新格式进行了守恒律、先验估计、稳定性、收敛性分析,证明了其在时间上达到二阶、在空间上达到四阶收敛精度.最后,通过一个数值算例验证了理论的正确性和格式的高效性.
