AN ADAPTIVE LOCAL GRID REFINEMENT BASED ON THE EXACT PEAK CAPTURE ANDOSCILLATION FREE SCHEME TO SOLVE TRANSPORT-EQUATIONS

An adaptive local grid refinement (ALGR) algorithm based on exact peak capture and oscillation free scheme (EPCOF) is developed to solve tra nsport equations. This algorithm consists of the Lagrangian-Eulerian d ecoupling of advection-diffusion transport, backward-node tracking, fo rward-node tracking, and adaptive local grid refinement based on exact peak capture and oscillation free strategies. Means of checking accum ulated mass-balance errors are provided. Application of the algorithm to four benchmark (two 1-D and two 2-D) problems under a variety of co nditions indicated that it completely eliminated peak clipping, spurio us oscillation, numerical diffusion, and grid-orientation difficulties . It yielded identical results, within the error tolerance, to exact s olutions for 35 of the 43 test cases; very good solutions, albeit not exact to within the error tolerance, were obtained for the remaining 8 cases. Accumulated mass-balance errors are very small for all cases w ith the maximum error of less than 1%. The proposed ALGR-EPCOF is also used to simulate a three-dimensional advective-diffusive-reactive tra nsport problem. Simulation results are accurate to within error tolera nce in comparison to exact solutions for the case of advective-reactiv e transport. This demonstrates that the use of tetrangulating the acti vated forward-tracked nodes is a promising one. The ALGR-EPCOF approac h could solve the advective-reactive transport problems exactly, withi n any prescribed error tolerance, using mesh Peclet numbers ranging fr om 0 to infinity and very large mesh Courant numbers in the Lagrangian -step computation. The size of the mesh Courant number is limited only by the accuracy requirement of the diffusion solver in the Eulerian-s tep computation. If the associated diffusion solver can solve the diff usion transport exactly within the same error tolerance, then the ALGR -EPCOF approach can solve the advection-diffusion-reactive problems ex actly to within the prescribed error tolerance.