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
This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is ...This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.展开更多
A "dual time" method for the solution of unsteady three dimensional Navier Stocks equations is described in this paper. An implicit real time discretisation is used, and then the equations are integrated in ...A "dual time" method for the solution of unsteady three dimensional Navier Stocks equations is described in this paper. An implicit real time discretisation is used, and then the equations are integrated in a fictitious pseudo time. When marching in a pseudo time, the finite volume method, multi grid scheme and other acceleration techniques used in steady flow calculations can be used. Balwin Lomax turbulence model is applied to simulate the turbulence.展开更多
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.
文摘This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.
文摘A "dual time" method for the solution of unsteady three dimensional Navier Stocks equations is described in this paper. An implicit real time discretisation is used, and then the equations are integrated in a fictitious pseudo time. When marching in a pseudo time, the finite volume method, multi grid scheme and other acceleration techniques used in steady flow calculations can be used. Balwin Lomax turbulence model is applied to simulate the turbulence.
