Space-time-unified GIRM (Generalized Integral Representation Method) for unsteady advective diffusion
This work addresses computational efficiency for solving unsteady advective diffusion problems, but the contribution appears incremental as it applies existing methods to a specific class of problems.
The paper discusses the Generalized Integral Representation Method (GIRM) for unsteady advective diffusion, comparing Space-Time-Separated and Space-Time-Unified methods. Numerical results for 2D problems using the unified method show satisfactory accuracy, though Neumann problems require smaller time increments.
The Generalized Integral Representation Method (GIRM) for Space-Time-Separated Method (STSM) and Space-Time-Unified Method (STUM) are discussed. STSM and STUM give explicit and implicit time evolutions, respectively. The algorithm of STSM is much simpler than STUM. However, the implicit time evolution of STUM could give us much more efficient computation. Numerical calculations using STUM for Dirichlet and Neumann problems in 2D space-time are conducted using a Traditional Fundamental Solution (TFS). The results seem very satisfactory. However, in case of Neumann problem, the time increment must be smaller than in case of Dirichlet problem.