Stable and accurate partitioned time integration methods for transport problems
A partitioned time integration method for advection-diffusion-reaction problems is presented. The spatial problem domain is decomposed into two non-overlapping sub-domains using dual-Schur domain decomposition. The decomposed discrete system is numerically expressed as a system of differential-algebraic equations (DAEs). The trapezoidal family of schemes is used to integrate the governing ordinary differential equations for each sub-domain. Different constraints enforcing the kinematic continuity of the solution across the interface between the subdomains are explored. A detailed error analysis is conducted for each choice of the constraint to evaluate the convergence of the numerical method. Conditions, under which the zero-order and first-order terms vanish, resulting in second-order accuracy, are derived. For the c-continuity method, the first order terms of c, v and λ are vanished by choosing γ A = γB = 0.5. For the v-continuity method, the zero-order and first order terms of c, v and λ are vanished by choosing γ A = γB = 0.5 . For the modified-c continuity method, the first-order term of c can be eliminated by choosing γ = 0.5 , the first order term of v and λ can be eliminated for γ = 1 ± √2/2. Finally, several numerical examples are presented to demonstrate the feasibility and performance of the partitioned time integration method.
Prakash, Purdue University.
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