Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(f...Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(for example,in analyzing the non-Darcy and anisotropic effects on the convection),such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer.Some solutions considering the anisotropic effect of permeability have been given previously by the authors,and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.展开更多
An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explic...An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.展开更多
Several families of algebraically explicit analytical wavesolutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families...Several families of algebraically explicit analytical wavesolutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. \{Among\} them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.50246003)NKBRSF(Grant No.G2000026305).
文摘Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(for example,in analyzing the non-Darcy and anisotropic effects on the convection),such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer.Some solutions considering the anisotropic effect of permeability have been given previously by the authors,and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.
基金Supported by the Natural Science Foundation of China under the grant 11026165 and 11072053Doctaral Fund of Ministry of Education of China under the grant 20100041120037the Fundamental Research Funds for the Central Universities
文摘An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 59846007, 59925615) NKBRSF (G1999022309, G2000026305).
文摘Several families of algebraically explicit analytical wavesolutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. \{Among\} them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.
