The Parabolic Spline Method (PSM) for conservative transport problems Export

@article{citeulike:1397421, abstract = {A new and efficient parabolic spline based remapping algorithm is developed and tested herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed parabolic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A grid and sub-grid based monotonic filter is also incorporated into the overall scheme. A truncation error analysis of the scheme is presented and discussed in terms of results from test cases. The analysis shows that although it has a similar truncation error in the converged limit as that of the widely used Piecewise Parabolic Method (PPM) for infinitely differentiable functions, PSM is more accurate than PPM for problems with slow spectral decay. Additionally, an operation count of the scheme is given which demonstrates the computational advantage of PSM compared to PPM. {\copyright} Crown copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley \& Sons, Ltd.}, address = {Met Office, FitzRoy Road, Exeter EX1 3PB, U.K.}, author = {Zerroukat, M. and Wood, N. and Staniforth, A.}, citeulike-article-id = {1397421}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.1154}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/112210446/ABSTRACT}, comment = {Parabolic Spline approach, global stencil...not a terribly parallel, but it's more accurate than PPM.}, doi = {10.1002/fld.1154}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {cascade, conservative, psm, semi-lagrangian}, number = {11}, pages = {1297--1318}, posted-at = {2007-06-18 18:41:34}, priority = {0}, title = {The Parabolic Spline Method (PSM) for conservative transport problems}, url = {http://dx.doi.org/10.1002/fld.1154}, volume = {51}, year = {2006} }

TY - JOUR ID - citeulike:1397421 L3 - citeulike-article-id:1397421 N2 - A new and efficient parabolic spline based remapping algorithm is developed and tested herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed parabolic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A grid and sub-grid based monotonic filter is also incorporated into the overall scheme. A truncation error analysis of the scheme is presented and discussed in terms of results from test cases. The analysis shows that although it has a similar truncation error in the converged limit as that of the widely used Piecewise Parabolic Method (PPM) for infinitely differentiable functions, PSM is more accurate than PPM for problems with slow spectral decay. Additionally, an operation count of the scheme is given which demonstrates the computational advantage of PSM compared to PPM. © Crown copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd. IS - 11 JF - International Journal for Numerical Methods in Fluids AD - Met Office, FitzRoy Road, Exeter EX1 3PB, U.K. EP - 1318 TI - The Parabolic Spline Method (PSM) for conservative transport problems VL - 51 SP - 1297 KW - cascade KW - conservative KW - psm KW - semi-lagrangian N1 - Parabolic Spline approach, global stencil...not a terribly parallel, but it's more accurate than PPM. AU - Zerroukat, M AU - Wood, N AU - Staniforth, A PY - 2006/// UR - http://dx.doi.org/10.1002/fld.1154 ER -