In this paper,we propose a second-order moving-water equilibria preserving nonstaggered central scheme to solve the Ripa model via flux globalization.To maintain the moving-water steady states,we use the discrete sour...In this paper,we propose a second-order moving-water equilibria preserving nonstaggered central scheme to solve the Ripa model via flux globalization.To maintain the moving-water steady states,we use the discrete source terms proposed by Britton et al.(J Sci Comput,2020,82(2):Art 30)by incorporating the expression of the source terms as a whole into the flux gradient,which directly avoids the discrete complexity of the source terms in order to maintain the well-balanced properties of the scheme.In addition,since the nonstaggered central scheme requires re-projecting the updated values of the nonstaggered cells onto the staggered cells,we modify the calculation of the global variables by constructing ghost cells and alternating the values of the global variables with the water depths obtained from the solution through the nonlinear relationship between the global flux and the water depth.In order to maintain the second-order accuracy of the scheme on the time scale,we incorporate a new Runge-Kutta type time discretization in the evolution of the numerical solution for the nonstaggered cells.Meanwhile,we introduce the"draining"time step technique to ensure that the water depth is positive and that it satisfies mass conservation.Numerical experiments verify that the scheme is well-balanced,positivity-preserving and robust.展开更多
In this paper,an extremal eigenvalue problem to the Sturm-Liouville equations with discontinuous coefficients and volume constraint is investigated.Liouville transformation is applied to change the problem into an equ...In this paper,an extremal eigenvalue problem to the Sturm-Liouville equations with discontinuous coefficients and volume constraint is investigated.Liouville transformation is applied to change the problem into an equivalent minimization problem.Finite element method is proposed and the convergence for the finite element solution is established.A monotonic decreasing algorithm is presented to solve the extremal eigenvalue problem.A global convergence for the algorithm in the continuous case is proved.A few numerical results are given to depict the efficiency of the method.展开更多
A fully higher-order compact(HOC)finite difference scheme on the 9-point two-dimensional(2D)stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure fi...A fully higher-order compact(HOC)finite difference scheme on the 9-point two-dimensional(2D)stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-Al2O3 nanofluid.Two cases are considered depending on the direction of temperature gradient imposed(Case I,top and bottom;Case II,left and right).The developed equations are given in terms of the stream function-vorticity formulation and are nondimensionalized and then solved numerically by a fourth-order accurate compact finite difference method.Unlike other compact solution procedure in literature for this physical configuration,the present method is fully compact and fully higher-order accurate.The fluid flow,heat transfer and heat transport characteristics were illustrated by streamlines,isotherms and averaged Nusselt number.Comparisons with previously published work are performed and found to be in excellent agreement.A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.展开更多
基金supported by the National Natural Science Foundation of China(51879194)。
文摘In this paper,we propose a second-order moving-water equilibria preserving nonstaggered central scheme to solve the Ripa model via flux globalization.To maintain the moving-water steady states,we use the discrete source terms proposed by Britton et al.(J Sci Comput,2020,82(2):Art 30)by incorporating the expression of the source terms as a whole into the flux gradient,which directly avoids the discrete complexity of the source terms in order to maintain the well-balanced properties of the scheme.In addition,since the nonstaggered central scheme requires re-projecting the updated values of the nonstaggered cells onto the staggered cells,we modify the calculation of the global variables by constructing ghost cells and alternating the values of the global variables with the water depths obtained from the solution through the nonlinear relationship between the global flux and the water depth.In order to maintain the second-order accuracy of the scheme on the time scale,we incorporate a new Runge-Kutta type time discretization in the evolution of the numerical solution for the nonstaggered cells.Meanwhile,we introduce the"draining"time step technique to ensure that the water depth is positive and that it satisfies mass conservation.Numerical experiments verify that the scheme is well-balanced,positivity-preserving and robust.
基金supported by the National Natural Science Foundation of China(10971159,91130022,11101316).
文摘In this paper,an extremal eigenvalue problem to the Sturm-Liouville equations with discontinuous coefficients and volume constraint is investigated.Liouville transformation is applied to change the problem into an equivalent minimization problem.Finite element method is proposed and the convergence for the finite element solution is established.A monotonic decreasing algorithm is presented to solve the extremal eigenvalue problem.A global convergence for the algorithm in the continuous case is proved.A few numerical results are given to depict the efficiency of the method.
基金supported by the National Natural Science Foundation of China(No.10971159).
文摘A fully higher-order compact(HOC)finite difference scheme on the 9-point two-dimensional(2D)stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-Al2O3 nanofluid.Two cases are considered depending on the direction of temperature gradient imposed(Case I,top and bottom;Case II,left and right).The developed equations are given in terms of the stream function-vorticity formulation and are nondimensionalized and then solved numerically by a fourth-order accurate compact finite difference method.Unlike other compact solution procedure in literature for this physical configuration,the present method is fully compact and fully higher-order accurate.The fluid flow,heat transfer and heat transport characteristics were illustrated by streamlines,isotherms and averaged Nusselt number.Comparisons with previously published work are performed and found to be in excellent agreement.A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.
