Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite vol...Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC[49,50].By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach,we efficiently achieve a fast convergence and reasonable solutions for this multiphase,multiphysics PEMFC model.Numerical implementation is done by using a novel automated finite element/finite volume programgenerator(FEPG).By virtue of a high-level algorithmdescription language(script),component programming and human intelligence technologies,FEPG can quickly generate finite element/finite volume source code for PEMFC simulation.Thus,one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods.Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D,multiphysics PEMFC model with multicomponent and multiphase mechanism.展开更多
We present a new splitting method for time-dependent convention-dominated diffusion problems.The original convention diffusion system is split into two sub-systems:a pure convection system and a diffusion system.At ea...We present a new splitting method for time-dependent convention-dominated diffusion problems.The original convention diffusion system is split into two sub-systems:a pure convection system and a diffusion system.At each time step,a convection problem and a diffusion problem are solved successively.A few important features of the scheme lie in the facts that the convection subproblem is solved explicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme;while the diffusion subproblem is always self-adjoint and coercive so that they can be solved efficiently using many existing optimal preconditioned iterative solvers.The scheme can be extended for solving the Navier-Stokes equations,where the nonlinearity is resolved by a linear explicit multistep scheme at the convection step,while only a generalized Stokes problem is needed to solve at the diffusion step and the major stiffness matrix stays invariant in the time marching process.Numerical simulations are presented to demonstrate the stability,convergence and performance of the single-step and multistep variants of the new scheme.展开更多
基金supported by NSF Grant DMS-0913757 and 111-Program for energysaving and environment-friendly automobile(B08019)of ChinaPengtao Sun was also partially supported by State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences during his visit in July,2010.Su Zhou is supported by 863 Program(2008AA050403)+2 种基金Shanghai Pujiang Talent Plan(08PJ1409)of China.Qiya Hu is supported by The Key Project of Natural Science Foundation of China G11031006National Basic Research Programof China G2011309702Natural Science Foundation of China G10771178.
文摘Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC[49,50].By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach,we efficiently achieve a fast convergence and reasonable solutions for this multiphase,multiphysics PEMFC model.Numerical implementation is done by using a novel automated finite element/finite volume programgenerator(FEPG).By virtue of a high-level algorithmdescription language(script),component programming and human intelligence technologies,FEPG can quickly generate finite element/finite volume source code for PEMFC simulation.Thus,one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods.Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D,multiphysics PEMFC model with multicomponent and multiphase mechanism.
基金The work of F.Shi was partially supported by NSFC(Projects 41104039 and 11401563)Guangdong Natural Science Foundation(Project S201204007760)+2 种基金Tianyuan Fund for Mathematics of the NSFC(Project 11226314)the Knowledge Innovation Program of the Chinese Academy of Sciences(China)under KJCX2-EW-L01,and the international cooperation project of Guangdong province(China)under 2011B050400037J.Zou was substantially supported by Hong Kong RGC grants(Projects 404611 and 405513)。
文摘We present a new splitting method for time-dependent convention-dominated diffusion problems.The original convention diffusion system is split into two sub-systems:a pure convection system and a diffusion system.At each time step,a convection problem and a diffusion problem are solved successively.A few important features of the scheme lie in the facts that the convection subproblem is solved explicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme;while the diffusion subproblem is always self-adjoint and coercive so that they can be solved efficiently using many existing optimal preconditioned iterative solvers.The scheme can be extended for solving the Navier-Stokes equations,where the nonlinearity is resolved by a linear explicit multistep scheme at the convection step,while only a generalized Stokes problem is needed to solve at the diffusion step and the major stiffness matrix stays invariant in the time marching process.Numerical simulations are presented to demonstrate the stability,convergence and performance of the single-step and multistep variants of the new scheme.
