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非定常Stokes方程一种基于POD方法的简化有限差分格式 总被引:1,自引:1,他引:0
特征正交分解(proper orthogonal decomposition,简记为POD)方法是一种可对偏微分方程的物理模型(如流体流动)做简化的技术.这种方法已经成功地用于对复杂系统模型降阶.推广应用POD方法,将POD方法应用于具有实际应用背景的非定常Stokes方程经典的有限差分格式,建立一种维数较低而精度足够高的简化差分格式,并给出简化差分格式解与经典差分格式解的误差估计.数值例子说明数值计算结果与理论结果相吻合.进一步表明基于POD方法的简化差分格式对求解非定常Stokes方程数值解是可行和有效的. 相似文献
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The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated. 相似文献
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IntroductionThoughatransport_diffusion (orLagrange_Galerkin)method ,whichisalsocalledachar_acteristicsmethod ,isanoldone[1]andhasbeenextensivelyappliedtodealingwithPDEswithdiffusiontermand/orconvection ,ithadnotbeenmixedthefiniteelementmethodstotreatsuccessfullytheconvergenceofnumericalsolutionfortheNavier_Stokesequationsuntiltheearly198 0s[2 ].Intheearly 1 990s,Berm挷dezetal.[3]appliedthismethodtodealingwiththeshallowwaterequationsonlyincludingthecurrentandthedepthofwaterandonlyderi… 相似文献
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A proper orthogonal decomposition(POD) method was successfully used in the reduced-order modeling of complex systems.In this paper,we extend the applications of POD method,namely,apply POD method to a classical finite element(FE) formulation for second-order hyperbolic equations with real practical applied background,establish a reduced FE formulation with lower dimensions and high enough accuracy,and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications.Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions.Moreover,it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations. 相似文献
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An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal. 相似文献
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本文证明了不完全双二次非协调板元离散的 Poincaré型不等式成立,利用它建立了类似于文的引理,从而由此讨论了边界固支薄板弯曲障碍问题和带平均曲率型约束问题的不完全双二次非协调板元逼近,得到了离散解对真解的收敛性并讨论了离散问题的迭代解。 相似文献
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