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A fast numerical method for solving coupled Burgers' equations

史峰 博士(哈尔滨工业大学深圳校区)
2014年12月01日(周一) 下午14:00-15:00  闵行数学楼102报告厅
 
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摘要: Burgers’ equation have the same convective and diffusion terms as
the incompressible Navier-Stokes equations, and is a much simple model for the understanding of physical flows and problems. Simulation of Burgers’
equation is a natural step towards developing methods for the computation of the complex flows.
In this talk, We present a new splitting method for coupled Burgers equation. 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 a 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.
Specially, the nonlinearity is resolved by a linear explicit multistep
scheme at the convection step, and all the stiffness matrices stay invariant
in the time marching process. Numerical simulations are presented to demonstrate the stability, convergence and performance of the the new
scheme.
   
 
 
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