Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensionalspace.Its symmetry groups and corresponding optimal systems are determined,and several classes of irrotational ...Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensionalspace.Its symmetry groups and corresponding optimal systems are determined,and several classes of irrotational groupinvariantsolutions associated to the symmetries are obtained and special case of one-dimensional rarefaction wave isfound.展开更多
In this paper,the authors use Glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial data.To this end,some important properties of the shock cur...In this paper,the authors use Glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial data.To this end,some important properties of the shock curves of the pressure-gradient system in the Riemann invariant coordinate system and verify that the shock curves satisfy Diperna’s conditions(see[Diperna,R.J.,Existence in the large for quasilinear hyperbolic conservation laws,Arch.Ration.Mech.Anal.,52(3),1973,244–257])are studied.Then they construct the approximate solution sequence through Glimm scheme.By establishing accurate local interaction estimates,they prove the boundedness of the approximate solution sequence and its total variation.展开更多
In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calcula...In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11071195 and 10926082China Postdoctoral Science Foundation under Grant No. 20090461305+1 种基金the National Natural Science Foundation of Shaanxi Province under Grant No. 2009JQ1003the Program of Shmunxi Provincial Department of Education under Grant Nos. 09JK770 and 11JK0482
文摘Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensionalspace.Its symmetry groups and corresponding optimal systems are determined,and several classes of irrotational groupinvariantsolutions associated to the symmetries are obtained and special case of one-dimensional rarefaction wave isfound.
基金supported by the National Natural Science Foundation of China(No.11671193)。
文摘In this paper,the authors use Glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial data.To this end,some important properties of the shock curves of the pressure-gradient system in the Riemann invariant coordinate system and verify that the shock curves satisfy Diperna’s conditions(see[Diperna,R.J.,Existence in the large for quasilinear hyperbolic conservation laws,Arch.Ration.Mech.Anal.,52(3),1973,244–257])are studied.Then they construct the approximate solution sequence through Glimm scheme.By establishing accurate local interaction estimates,they prove the boundedness of the approximate solution sequence and its total variation.
文摘In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.
