The Experts below are selected from a list of 11247 Experts worldwide ranked by ideXlab platform
N V Nikitin - One of the best experts on this subject based on the ideXlab platform.
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finite difference method for incompressible navier stokes equations in arbitrary orthogonal curvilinear coordinates
Journal of Computational Physics, 2006Co-Authors: N V NikitinAbstract:A finite-difference method for solving three-dimensional time-dependent incompressible Navier-Stokes equations in arbitrary curvilinear orthogonal coordinates is presented. The method is oriented on turbulent flow simulations and consists of a second-order central difference approximation in space and a third-order semi-implicit Runge-Kutta Scheme for time advancement. Spatial discretization retains some important properties of the Navier-Stokes equations, including energy conservation by the nonlinear and pressure-gradient terms. Numerical tests cover Cartesian, cylindrical-polar, spherical, cylindrical elliptic and cylindrical bipolar coordinate systems. Both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method.
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third order accurate semi implicit runge Kutta Scheme for incompressible navier stokes equations
International Journal for Numerical Methods in Fluids, 2006Co-Authors: N V NikitinAbstract:A semi-implicit three-step Runge-Kutta Scheme for the unsteady incompressible Navier-Stokes equations with third-order accuracy in time is presented. The higher order of accuracy as compared to the existing semi-implicit Runge-Kutta Schemes is achieved due to one additional inversion of the implicit operator / - τγL, which requires inversion of tridiagonal matrices when using approximate factorization method. No additional solution of the pressure-Poisson equation or evaluation of Navier-Stokes operator is needed. The Scheme is supplied with a local error estimation and time-step control algorithm. The temporal third-order accuracy of the Scheme is proved analytically and ascertained by analysing both local and global errors in a numerical example.
Qing Huo Liu - One of the best experts on this subject based on the ideXlab platform.
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Efficient implicit-explicit time stepping Scheme with domain decomposition for multiscale modeling of layered structures
IEEE Transactions on Components Packaging and Manufacturing Technology, 2011Co-Authors: Jiefu Chen, Luis Eduardo Tobón, Mei Chai, Jason A. Mix, Qing Huo LiuAbstract:An efficient time-domain technique is proposed for multiscale electromagnetic simulations of layered structures. Each layer of a layered structure is independently discretized by finite elements, and the discontinuous Galerkin method is employed to stitch all discretized subdomains together. The hybrid implicit-explicit Runge-Kutta Scheme combined with subdomain-based Gauss-Seidel iteration is employed for time stepping. The block Thomas algorithm is utilized to accelerate time stepping for block tri-diagonal systems, which are frequently encountered in discretized layered structures. Numerical examples demonstrate that the proposed method is efficient in simulating multiscale layered structures.
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a 3 d discontinuous spectral element time domain method for maxwell s equations
IEEE Transactions on Antennas and Propagation, 2009Co-Authors: Joonho Lee, Jiefu Chen, Qing Huo LiuAbstract:A discontinuous spectral element time-domain method is proposed to analyze transient electromagnetic properties of general 3-D structures. This method is advantageous in that its mass matrices are block-diagonal due to the Gauss-Lobatto-Legendre polynomials, and it allows different orders of basis functions for each subdomain. The Riemann solver is employed in the boundary integral terms to communicate fields between adjacent subdomains. Perfectly matched layers are utilized to truncate the computational domain. Galerkin method is used for spatial discretization, and a fourth-order Runge-Kutta Scheme is employed for the time integration. The validity of the proposed approach is demonstrated through several numerical examples of initial value problems and scattering problems.
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a 3 d spectral element time domain method for electromagnetic simulation
IEEE Transactions on Microwave Theory and Techniques, 2007Co-Authors: Joonho Lee, Qing Huo LiuAbstract:A spectral-element time-domain (SETD) method is proposed to solve 3-D transient electromagnetic problems based on Gauss-Lobatto-Legendre polynomials. It has the advantages of spectral accuracy and block-diagonal mass matrix. With the inexpensive inversion of the block-diagonal mass matrix, the proposed method requires only a trivial sparse matrix-vector product at each time step, thus significantly reducing CPU time and memory requirement. Galerkin's method is used for spatial discretization, and a fourth-order Runge-Kutta Scheme is employed for the time integration. The perfectly matched layer (PML) is employed to truncate the boundary in unbounded problems. The pseudospectral time-domain method is used to simplify the treatment of the PML inside the proposed SETD method. Numerical examples are shown to verify the efficiency and the spectral accuracy with the order of basis functions
Daniel S Weile - One of the best experts on this subject based on the ideXlab platform.
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implicit runge Kutta methods for the discretization of time domain integral equations
IEEE Transactions on Antennas and Propagation, 2011Co-Authors: Xiaobo Wang, Daniel S WeileAbstract:Implicit Runge-Kutta based Schemes are proposed for solving the time domain integral equations of electromagnetic theory. The proposed technique maps a Laplace-domain equation to a Ƶ-domain equation using the Butcher tableau of the implicit Runge-Kutta Scheme. A discrete time domain system is recovered by computing the inverse Ƶ-transform numerically. The resulting technique is capable of third- or fifth-order accuracy in time, and is stable independent of time step. Numerical results illustrate the accuracy and stability of the technique.
Fabrice Mahe - One of the best experts on this subject based on the ideXlab platform.
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embedded runge Kutta Scheme for step size control in the interaction picture method
Computer Physics Communications, 2013Co-Authors: Stephane Balac, Fabrice MaheAbstract:Abstract When solving certain evolution type PDEs such as the Schrodinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge–Kutta Scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge–Kutta Scheme with orders 3 and 4 with the aim to deliver an estimation of the local error for adaptive step-size control purposes in the Interaction Picture method. The corresponding ERK4(3)-IP method preserves the features of the RK4-IP method and provides a local error estimate at no significant extra cost.
Lih-sheng Turng - One of the best experts on this subject based on the ideXlab platform.
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effect of centerline distance on mixing of a non newtonian fluid in a cavity with asymmetric rotors
Physics of Fluids, 2019Co-Authors: Yao Liu, Lih-sheng Turng, Chuntai LiuAbstract:Mixing of highly viscous fluids in a cavity with internal moving parts is a common scenario found in many engineering applications. It provides a challenge for numerical simulations. In this paper, asymmetric rotors were designed to enhance mixing, and the effect of different centerline distances on mixing was investigated numerically. The novel rotors co-rotate at a speed ratio of 2 and hence have different geometries to meet the requirement of self-cleaning. The finite element method was used to solve the time-dependent flow, in which the mesh superposition technique was used to include the internal moving parts in the fixed meshes of the flow domain. A non-Newtonian fluid obeying the Carreau–Yasuda constitutive model was used. A standard fourth-order Runge–Kutta Scheme was successfully developed to perform the particle tracking calculations. Distributive mixing was examined through the flow patterns and spatial positions of the tracked particles. The centerline distance was the key factor for controlling the gap between the rotors that influence mixing and energy consumption. Different mixing subzones alternated in sequence. On the one hand, this gap introduced a bifurcation in the intermeshing zone. On the other hand, stretching, folding, and reorientations, as well as cutting and dividing actions, were encountered in the sequence. This procedure was similar to a Baker’s transformation. By contrast, for a Newtonian fluid, mixing became worse and consumed slightly more energy.Mixing of highly viscous fluids in a cavity with internal moving parts is a common scenario found in many engineering applications. It provides a challenge for numerical simulations. In this paper, asymmetric rotors were designed to enhance mixing, and the effect of different centerline distances on mixing was investigated numerically. The novel rotors co-rotate at a speed ratio of 2 and hence have different geometries to meet the requirement of self-cleaning. The finite element method was used to solve the time-dependent flow, in which the mesh superposition technique was used to include the internal moving parts in the fixed meshes of the flow domain. A non-Newtonian fluid obeying the Carreau–Yasuda constitutive model was used. A standard fourth-order Runge–Kutta Scheme was successfully developed to perform the particle tracking calculations. Distributive mixing was examined through the flow patterns and ...
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numerical simulation of chaotic mixing in single screw extruders with different baffle heights
International Polymer Processing, 2016Co-Authors: B P Xu, M G Wang, H W Yu, L He, Lih-sheng TurngAbstract:Abstract A kind of discontinuous baffle, which had the same length as the non-baffle zone distance, was inserted in the unwound channel of a single screw extruder to enhance mixing in the screw channel. The periodic unit of the flow channel was modeled as a dynamic system of complex duct flow. The finite volume method was used to solve the three-dimensional flow of purely viscous non-Newtonian fluid. Fluid particle tracking was performed by a fourth-order Runge–Kutta Scheme. The effect of the baffle height on the mixing kinematics was investigated numerically. Poincare sections were applied to reveal the different patterns and sizes of the KAM tubes. Distributive mixing was then visualized by the evolution of passive tracers initially located at different positions. The variance index and residence time distribution (RTD) were used to evaluate the statistical results. Among the four test cases, the results showed that the case with the baffle height equal to the screw depth had the largest chaotic mixing ...
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chaotic mixing in a single screw extruder with a moving internal baffle
Polymer Engineering and Science, 2014Co-Authors: Yuejun Liu, Lih-sheng TurngAbstract:A geometry in which the mixing of a single-screw extruder was enhanced by a reciprocating baffle is proposed in this article. The effect of the baffle’s amplitude on the mixing kinematics of the screw channel was investigated. A model with the baffle lower than the screw channel and the corresponding mathematical model were developed. The periodic flow and mixing performance of Newtonian fluid in such an extruder were numerically simulated. The finite volume method was used, and the flow domain was meshed by staggered grids with the periodic boundary conditions of the barrier motion being imposed by the mesh supposition technique. Fluid particle tracking was performed by a fourth-order Runge‐Kutta Scheme. Distributive mixing was visualized by the evolution of passive tracers initially located at different positions. The growth of the interface stretch of tracers with time and the cumulative residence time distribution were also
