A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability o...A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake ortsunami waves in the deep ocean. The method combines a quasi-Lagrange movingmesh DG method, a hydrostatic reconstruction technique, and a change of unknownvariables. The strategies in the use of slope limiting, positivity-preservation limiting,and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treatsmesh movement continuously in time and has the advantages that it does not need tointerpolate flow variables from the old mesh to the new one and places no constraintfor the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method andits ability to adapt the mesh according to features in the flow and bottom topography.展开更多
Based on the final analysis data with horizontal resolution of 1°× 1°(four times a day) from the National Centers for Environmental Prediction(NCEP), a typical Northeast China cold vortex(NCCV) during t...Based on the final analysis data with horizontal resolution of 1°× 1°(four times a day) from the National Centers for Environmental Prediction(NCEP), a typical Northeast China cold vortex(NCCV) during the spring of 2010 was examined with the quasi-Lagrange- form eddy flux circulation(EFC) budget equation. Results indicated that the mechanisms that account for the development, maintenance, and attenuation of the cyclone varied with levels and stages. Displacement of the cyclone and transports by background environmental circulations dominated the variation of the cyclone in the middle and upper levels, whereas displacement and divergence associated with the cyclone dominated the evolution of the NCCV in the middle and lower levels. Moreover, interactions between the NCCV and other subsynoptic weather systems were important for the development of the cyclone, and the pattern of background environmental circulations was also important for the evolution of the NCCV, since the cyclone enhanced(weakened) as it moved from areas of low(high) vorticity to high(low) ones.展开更多
基金J.Qiu is supported partly by National Natural Science Foundation(China)grant 12071392.
文摘A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake ortsunami waves in the deep ocean. The method combines a quasi-Lagrange movingmesh DG method, a hydrostatic reconstruction technique, and a change of unknownvariables. The strategies in the use of slope limiting, positivity-preservation limiting,and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treatsmesh movement continuously in time and has the advantages that it does not need tointerpolate flow variables from the old mesh to the new one and places no constraintfor the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method andits ability to adapt the mesh according to features in the flow and bottom topography.
基金supported by the National Natural Science Foundation of China (Grant No. 41205027)the National Key Basic Research Program of China (Grant No. 2012CB 417201)
文摘Based on the final analysis data with horizontal resolution of 1°× 1°(four times a day) from the National Centers for Environmental Prediction(NCEP), a typical Northeast China cold vortex(NCCV) during the spring of 2010 was examined with the quasi-Lagrange- form eddy flux circulation(EFC) budget equation. Results indicated that the mechanisms that account for the development, maintenance, and attenuation of the cyclone varied with levels and stages. Displacement of the cyclone and transports by background environmental circulations dominated the variation of the cyclone in the middle and upper levels, whereas displacement and divergence associated with the cyclone dominated the evolution of the NCCV in the middle and lower levels. Moreover, interactions between the NCCV and other subsynoptic weather systems were important for the development of the cyclone, and the pattern of background environmental circulations was also important for the evolution of the NCCV, since the cyclone enhanced(weakened) as it moved from areas of low(high) vorticity to high(low) ones.
