TY - JOUR
T1 - An adaptive local grid refinement based on the exact peak capture and oscillation free scheme to solve transport equations
AU - Yeh, Gour Tsyh
AU - Chang, Jing Ru
AU - Cheng, Hwai Ping
AU - Sung, Chao Ho
N1 - Funding Information:
Acknowledgements-Thrise searchis supportedi,n part,b y Applied ResearchL aboratoryt, heP ennsylvaniSat ateU niversity and, in part, by the Office of Health and EnvironmentalR esearch,D epartmento f Energy, Grant No. DE-FGOZ-9lER61197C. PU timew asp rovidedb y theN ationalA erodynamicS imulationP rograma t NASA, Ames ResearchC enter.
PY - 1995/3
Y1 - 1995/3
N2 - An adaptive local grid refinement (ALGR) algorithm based on exact peak capture and oscillation free scheme (EPCOF) is developed to solve transport equations. This algorithm consists of the Lagrangian-Eulerian decoupling of advection-diffusion transport, backward-node tracking, forwardnode tracking, and adaptive local grid refinement based on exact peak capture and oscillation free strategies. Means of checking accumulated mass-balance errors are provided. Application of the algorithm to four benchmark (two 1-D and two 2-D) problems under a variety of conditions indicated that it completely eliminated peak clipping, spurious oscillation, numerical diffusion, and grid-orientation difficulties. It yielded identical results, within the error tolerance, to exact solutions 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 with the maximum error of less than 1%. The proposed ALGR-EPCOF is also used to simulate a three-dimensional advective-diffusive-reactive transport problem. Simulation results are accurate to within error tolerance in comparison to exact solutions for the case of advective-reactive transport. This demonstrates that the use of tetrangulating the activated forward-tracked nodes is a promising one. The ALGR-EPCOF approach could solve the advective-reactive transport problems exactly, within any prescribed error tolerance, using mesh Peclet numbers ranging from 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-step computation. If the associated diffusion solver can solve the diffusion transport exactly within the same error tolerance, then the ALGR-EPCOF approach can solve the advection-diffusion-reactive problems exactly to within the prescribed error tolerance.
AB - An adaptive local grid refinement (ALGR) algorithm based on exact peak capture and oscillation free scheme (EPCOF) is developed to solve transport equations. This algorithm consists of the Lagrangian-Eulerian decoupling of advection-diffusion transport, backward-node tracking, forwardnode tracking, and adaptive local grid refinement based on exact peak capture and oscillation free strategies. Means of checking accumulated mass-balance errors are provided. Application of the algorithm to four benchmark (two 1-D and two 2-D) problems under a variety of conditions indicated that it completely eliminated peak clipping, spurious oscillation, numerical diffusion, and grid-orientation difficulties. It yielded identical results, within the error tolerance, to exact solutions 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 with the maximum error of less than 1%. The proposed ALGR-EPCOF is also used to simulate a three-dimensional advective-diffusive-reactive transport problem. Simulation results are accurate to within error tolerance in comparison to exact solutions for the case of advective-reactive transport. This demonstrates that the use of tetrangulating the activated forward-tracked nodes is a promising one. The ALGR-EPCOF approach could solve the advective-reactive transport problems exactly, within any prescribed error tolerance, using mesh Peclet numbers ranging from 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-step computation. If the associated diffusion solver can solve the diffusion transport exactly within the same error tolerance, then the ALGR-EPCOF approach can solve the advection-diffusion-reactive problems exactly to within the prescribed error tolerance.
UR - http://www.scopus.com/inward/record.url?scp=0029274661&partnerID=8YFLogxK
U2 - 10.1016/0045-7930(94)00033-U
DO - 10.1016/0045-7930(94)00033-U
M3 - 期刊論文
AN - SCOPUS:0029274661
SN - 0045-7930
VL - 24
SP - 293
EP - 332
JO - Computers and Fluids
JF - Computers and Fluids
IS - 3
ER -