The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
Zhen F Tian - One of the best experts on this subject based on the ideXlab platform.
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compact computations based on a Stream Function velocity formulation of two dimensional steady laminar natural convection in a square cavity
Physical Review E, 2012Co-Authors: Pei Xiang Yu, Zhen F TianAbstract:: A class of compact second-order finite difference algorithms is proposed for solving steady-state laminar natural convection in a square cavity using the Stream-Function-velocity (ψ-u) form of Navier-Stokes equations. The Stream-Function-velocity equation and the energy equation are all solved as a coupled system of equations for the four field variables consisting of Stream Function, two velocities, and temperature. Two strategies are considered for the discretizaton of the temperature equation, which are a second-order five-point compact scheme and a fourth-order nine-point compact scheme, respectively. The numerical capability of the presented algorithm is demonstrated by the application to natural convection in a square enclosure for a wide range of Rayleigh numbers (from 10(3) to 10(8)) and compared with some of the accurate results available in the literature. The presented schemes not only show second-order accurate, but also prove effective. For larger Rayleigh numbers, the algorithm combining the second-order compact scheme for the Stream-Function-velocity equation with the fourth-order compact scheme for the temperature equation performs more stably and effectively.
Chris Wojtan - One of the best experts on this subject based on the ideXlab platform.
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a Stream Function solver for liquid simulations
International Conference on Computer Graphics and Interactive Techniques, 2015Co-Authors: Ryoichi Ando, Nils Thuerey, Chris WojtanAbstract:This paper presents a liquid simulation technique that enforces the incompressibility condition using a Stream Function solve instead of a pressure projection. Previous methods have used Stream Function techniques for the simulation of detailed single-phase flows, but a formulation for liquid simulation has proved elusive in part due to the free surface boundary conditions. In this paper, we introduce a Stream Function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling. Although our approach increases the dimension of the linear system necessary to enforce incompressibility, it provides interesting and surprising benefits. First, the resulting flow is guaranteed to be divergence-free regardless of the accuracy of the solve. Second, our free-surface boundary conditions guarantee divergence-free motion even in the un-simulated air phase, which enables two-phase flow simulation by only computing a single phase. We implemented this method using a variant of FLIP simulation which only samples particles within a narrow band of the liquid surface, and we illustrate the effectiveness of our method for detailed two-phase flow simulations with complex boundaries, detailed bubble interactions, and two-way solid-fluid coupling.
D K Ganjoo - One of the best experts on this subject based on the ideXlab platform.
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incompressible flow computations based on the vorticity Stream Function and velocity pressure formulations
Computers & Structures, 1990Co-Authors: Tayfun E Tezduyar, J Liou, D K GanjooAbstract:Abstract Finite element procedures and computations based on the velocity-pressure and vorticityStream Function formulations of incompressible flows are presented. Two new multi-step velocity-pressure formulations are proposed and are compared with the vorticity-Stream Function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-Stream Function formulation and one of the two new multi-step formulations involve much less numerical dissipation than the one-step formulation.
Pei Xiang Yu - One of the best experts on this subject based on the ideXlab platform.
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compact computations based on a Stream Function velocity formulation of two dimensional steady laminar natural convection in a square cavity
Physical Review E, 2012Co-Authors: Pei Xiang Yu, Zhen F TianAbstract:: A class of compact second-order finite difference algorithms is proposed for solving steady-state laminar natural convection in a square cavity using the Stream-Function-velocity (ψ-u) form of Navier-Stokes equations. The Stream-Function-velocity equation and the energy equation are all solved as a coupled system of equations for the four field variables consisting of Stream Function, two velocities, and temperature. Two strategies are considered for the discretizaton of the temperature equation, which are a second-order five-point compact scheme and a fourth-order nine-point compact scheme, respectively. The numerical capability of the presented algorithm is demonstrated by the application to natural convection in a square enclosure for a wide range of Rayleigh numbers (from 10(3) to 10(8)) and compared with some of the accurate results available in the literature. The presented schemes not only show second-order accurate, but also prove effective. For larger Rayleigh numbers, the algorithm combining the second-order compact scheme for the Stream-Function-velocity equation with the fourth-order compact scheme for the temperature equation performs more stably and effectively.
G F Carey - One of the best experts on this subject based on the ideXlab platform.
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Stream Function vorticity driven cavity solution using p finite elements
Computers & Fluids, 1997Co-Authors: E Barragy, G F CareyAbstract:Calculations for the two-dimensional driven cavity incompressible flow problem are presented. A p-type finite element scheme for the fully coupled Stream Function-vorticity formulation of the Navier-Stokes equations is used. Graded meshes are used to resolve vortex flow features and minimize the impact of corner singularities. Incremental continuation in the Reynolds number allows solutions to be computed for Re = 12 500. A significant feature of the work is that new tertiary and quaternary corner vortex features are observed in the flow field. Comparisons are made with other solutions in the literature.
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high order compact scheme for the steady Stream Function vorticity equations
International Journal for Numerical Methods in Engineering, 1995Co-Authors: W F Spotz, G F CareyAbstract:A higher-order compact scheme that is O(h4) on the nine-point 2-D stencil is formulated for the steady Stream-Function vorticity form of the Navier-Stokes equations. The resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software. We also show that special treatment of the wall boundary conditions is required. The method is tested on representative model problems and compares very favourably with other schemes in the literature.
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iterative solution of the Stream Function vorticity equations using a multigrid solver with finite elements
Communications in Numerical Methods in Engineering, 1993Co-Authors: M B Davis, G F CareyAbstract:The solution of the Stream Function–vorticity equations is developed using a multigrid method to improve efficiency in a finite-element p-method. The equations are discretized using 2-D Lagrange finite elements (linear, quadratic and cubic) and solved in iteratively decoupled form using successive approximation and continuation methods. The comparative performance of several multigrid and direct matrix solvers is investigated with respect to convergence characteristics and time performance on the Cray Y-MP.
