BALANCED SPLITTING AND REBALANCED SPLITTING

作者：Speth Raymond L^*; Green William H; Macnamara Shev; Strang Gilbert

来源：SIAM Journal on Numerical Analysis, 2013, 51(6): 3084-3105.

DOI：10.1137/120878641

• Strang splitting
• steady state
• advection-diffusion
• reaction
• combustion

Many systems of equations fit naturally in the form du/dt = A(u) + B(u). We may separate convection from diffusion, x-derivatives from y-derivatives, and (especially) linear from nonlinear. We alternate between integrating operators for dv/dt = A(v) and dw/dt = B(w). Non-commutativity (in the simplest case, of e(Ah) and e(Bh)) introduces a splitting error which persists even in the steady state. Second-order accuracy can be obtained by placing the step for B between two half-steps of A. This splitting method is popular, and we suggest a possible improvement, especially for problems that converge to a steady state. Our idea is to adjust the splitting at each timestep to [A(u) + c(n)] + [B(u) - c(n)]. We introduce two methods, balanced splitting and rebalanced splitting, for choosing the constant c(n). The execution of these methods is straightforward, but the stability analysis becomes more difficult than for c(n) = 0. Experiments with the proposed rebalanced splitting method indicate that it is much more accurate than conventional splitting methods as systems approach steady state. This should be useful in large-scale simulations (e. g., reacting flows). Further exploration may suggest other choices for c(n) which work well for different problems.

• 出版日期2013