The Experts below are selected from a list of 10311 Experts worldwide ranked by ideXlab platform
Phillip Colella - One of the best experts on this subject based on the ideXlab platform.
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A Cartesian Grid Embedded Boundary Method for the Heat Equation and Poisson's
2020Co-Authors: Peter Schwartz, Phillip Colella, Michael F Barad, Terry J LigockiAbstract:We present an algorithm for solving Poisson’s equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian Grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60‐85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60‐85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian Grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multiGrid solvers.
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a fourth order boundary treatment for viscous fluxes on Cartesian Grid finite volume methods
52nd Aerospace Sciences Meeting, 2014Co-Authors: Stephen M Guzik, Phillip ColellaAbstract:This study focuses on a fourth-order boundary treatment for nite-volume schemes to solve the compressible Navier-Stokes equations on a Cartesian Grid. A fourth-order nite-volume stencil is derived for the viscous stress tensor operator and the modi ed fourth-order stencil near the physical boundary is developed. Fourier error analysis and stability analysis are performed for the fourth-order elliptic operator. For time integration, we use the fourth-order Runge-Kutta method. The fourth-order scheme was applied to the transient Couette ow and the solution accuracy was veri ed.
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a Cartesian Grid embedded boundary method for the heat equation and poisson s equation in three dimensions
Journal of Computational Physics, 2006Co-Authors: Peter Schwartz, Phillip Colella, Michael F Barad, Terry J LigockiAbstract:We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian Grid embedded boundary algorithm for 2D problems of Johansen and Colella [A Cartesian Grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys. 147(2) (1998) 60-85] and extends work of McCorquodale, Colella and Johansen [A Cartesian Grid embedded boundary method for the heat equation on irregular domains, J. Comput. Phys. 173 (2001) 620-635]. Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian Grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multiGrid solvers.
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a Cartesian Grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics, 2006Co-Authors: Phillip Colella, Daniel T Graves, Benjamin Keen, David ModianoAbstract:We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume Grid obtained from intersecting the domain with a Cartesian Grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L^1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
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a Cartesian Grid embedded boundary method for the heat equation and poisson s equation in three dimensions
Lawrence Berkeley National Laboratory, 2004Co-Authors: Peter Schwartz, Phillip Colella, Michael F Barad, Terry J LigockiAbstract:A Cartesian Grid Embedded Boundary Method for the Heat Equation and Poisson’s Equation in Three Dimensions 1,2,3 Peter Schwartz ∗ ,1,3 , Michael Barad 2 , Phillip Colella 1,3 , Terry Ligocki 3 Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720 3 Department of Civil and Environmental Engineering, University of California, Davis, California 95616 2 Abstract We present an algorithm for solving Poisson’s equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian Grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60–85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60–85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian Grid cells with the domain, combined with a second-order accurate dis- cretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multiGrid solvers. Key words: Poisson Equation, Heat Equation, MultiGrid Methods PACS: 02.60.Lj, 02.70.Bf, 41.05.+e, 41.20.Cv ∗ Corresponding author Email address: poschwartz@lbl.gov (Peter Schwartz). 1 Supported by the DARPA BioComp program. 2 Supported by the Computational Science Graduate Fellowship program of the Depart- ment of Energy, under grant number DE-FG02-97ER25308. 3 Supported at the Lawrence Berkeley National Laboratory by the U.S Department of Energy: Director, Office of Science, Office of Advanced Scientific Computing, Mathematical, Information, and Computing Sciences Division under Contract DE-AC03-76SF00098. Preprint submitted to Elsevier Science 2 November 2004
H S Udaykumar - One of the best experts on this subject based on the ideXlab platform.
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a Cartesian Grid solver for simulation of a phase change material pcm solar thermal storage device
Numerical Heat Transfer Part B-fundamentals, 2016Co-Authors: Mike Augspurger, H S UdaykumarAbstract:ABSTRACTA Cartesian Grid solver is developed that is capable of simulating the convection-dominated melting processes in a latent-heat thermal storage device (TSD). The Navier-Stokes equations are solved using a dynamically refined mesh. The phase boundary is tracked using the enthalpy method. Conjugate heat transfer is calculated with a strongly coupled implicit scheme. The approach does not require the creation of a geometry-specific Grid, and so allows for efficient prototyping of different complex geometric designs. Systematic benchmarking of the results against other numerical approaches is conducted, followed by tests of two basic prototypes for the design of a TSD.
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adaptively refined parallelised sharp interface Cartesian Grid method for three dimensional moving boundary problems
International Journal of Computational Fluid Dynamics, 2009Co-Authors: H S Udaykumar, S Krishnan, Saikrishna V MarellaAbstract:Sharp interface Cartesian Grid methods are capable of simulating complex moving boundary problems on fixed meshes while treating embedded interfaces accurately. This article further enhances the effectiveness of the sharp interface method by devising techniques for adaptive mesh resolution combined with parallel processing. These extensions enable dealing with problems involving disparate length scales encountered in many applications. A tree-based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian Grid method for efficient and optimised calculations. Detailed timing and accuracy data are presented for a variety of benchmark problems involving moving boundaries. Guidelines for selecting mesh refinement criteria for moving boundary calculations are developed. Issues associated with parallelisation of the overall framework are tackled. The capabilities of the method are demonstrated in a number of moving boundary problems, which require adequate resolution of a wide range of length scales and three-dimensional flows.
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sharp interface Cartesian Grid method iii solidification of pure materials and binary solutions
Journal of Computational Physics, 2005Co-Authors: Yi Yang, H S UdaykumarAbstract:A numerical technique is presented for computing dendritic growth of crystals from pure melts and binary solutions. The governing equations are solved on a fixed Cartesian mesh and the immersed phase boundary is treated as a sharp solid-fluid interface. The interface is tracked using a level-set field. A finite-difference scheme is presented that incorporates the immersed phase boundary with only a small change to a standard Cartesian Grid Poisson solver. The scheme is simple to implement in three-dimensions. The results from our calculations show excellent agreement with two-dimensional microscopic solvability theory for pure material solidification. It is shown that the method predicts dendrite tip characteristics in excellent agreement with the theory. The sharp interface treatment allows discontinuous material property variation at the solid-liquid interface. This facilitates sharp-interface simulations of dendritic solidification of binary solutions.
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a sharp interface Cartesian Grid methodfor simulating flows with complexmoving boundaries
2001Co-Authors: H S Udaykumar, Rajat Mittal, P Rampunggoon, A KhannaAbstract:A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries H. S. Udaykumar,∗ R. Mittal,† P. Rampunggoon,‡ and A. Khanna∗ ∗Department of Mechanical Engineering, University of Iowa, Iowa City, Iowa 52242; †Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC 20052; and ‡Department of Mechanical Engineering, University of Florida, Gainesville, Florida 32611 E-mail: mittal@seas.gwu.edu
Donna Calhoun - One of the best experts on this subject based on the ideXlab platform.
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a Cartesian Grid method for solving the two dimensional streamfunction vorticity equations in irregular regions
Journal of Computational Physics, 2002Co-Authors: Donna CalhounAbstract:We describe a method for solving the two-dimensional Navier?Stokes equations in irregular physical domains. Our method is based on an underlying uniform Cartesian Grid and second-order finite-difference/finite-volume discretizations of the streamfunction-vorticity equations. Geometry representing stationary solid obstacles in the flow domain is embedded in the Cartesian Grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells. Along the embedded boundary, we determine a distribution of vorticity sources needed to impose the no-slip flow conditions. This distribution appears as a right-hand-side term in the discretized fluid equations, and so we can use fast solvers to solve the linear systems that arise. To handle the advective terms, we use the high-resolution algorithms in CLAWPACK. We show that our Stokes solver is second-order accurate for steady state solutions and that our full Navier?Stokes solver is between first- and second-order accurate and reproduces results from well-studied benchmark problems in viscous fluid flow. Finally, we demonstrate the robustness of our code on flow in a complex domain.
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a Cartesian Grid finite volume method for the advection diffusion equation in irregular geometries
Journal of Computational Physics, 2000Co-Authors: Donna Calhoun, Randall J LevequeAbstract:We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian Grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web.
Zhihui Li - One of the best experts on this subject based on the ideXlab platform.
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Cartesian Grid method for gas kinetic scheme on irregular geometries
Journal of Computational Physics, 2016Co-Authors: Songze Chen, Kun Xu, Zhihui LiAbstract:A Cartesian Grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the boundaries are represented by a set of direction-oriented boundary points, and the computational Grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We adopt a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian Grid method and the simplified flux solver. The reconstruction scheme for recovering the boundary conditions of compressible viscous and heat conducting flow with a Cartesian mesh can provide a smooth distribution of physical quantities at solid boundary, and present an accurate solution for the flow study with complex geometry.
Michael Welcome - One of the best experts on this subject based on the ideXlab platform.
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an adaptive Cartesian Grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics, 1995Co-Authors: R B Pember, Phillip Colella, William Y Curtchfield, John B Bell, Michael WelcomeAbstract:In this paper we describe an adaptive Cartesian Grid method for modeling time-dependent inviscid compressible flow in irregular regions. In this approach a body is treated as an interface embedded in a regular Cartesian mesh. The single Grid algorithm uses an unsplit second-order Godunov algorithm followed by a corrector applied to cells at the boundary. The discretization near the fluid-body interface is based on a volume-of-fluid approach with a redistribution procedure to maintain conservation while avoiding time step restrictions arising from small cells where the boundary intersects the mesh. The single Grid Cartesian mesh integration scheme is coupled to a conservative adaptive mesh refinement algorithm that selectively refines regions of the computational Grid to achieve a desired level of accuracy. Examples showing the results of the combined Cartesian Grid integration/adaptive mesh refinement algorithm for both two- and three-dimensional flows are presented.
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adaptive Cartesian Grid methods for representing geometry in inviscid compressible flow
11th Computational Fluid Dynamics Conference, 1993Co-Authors: R B Pember, Michael Welcome, John B Bell, W Y Crutchfield, Phillip ColellaAbstract:In this paper we describe a Cartesian Grid algorithm for modeling time-dependent compressible flow in complex geometry. In this approach problem geometry is treated as an interface embedded in a regular Cartesian mesh. The discretization near the embedded boundary is based on a volume-of-fluid approach with a redistribution procedure to avoid time-step restrictions arising from small cells where the boundary intersects the mesh. The algorithm is coupled to an unsplit second-order Godunov algorithm and is fully conservative, maintaining conservation at the boundary. The Godunov/Cartesian Grid integration scheme is coupled to a local adaptive mesh refinement algorithm that selectively refines regions of the computational Grid to achieve a desired level of accuracy. Examples showing the results of the combined Cartesian Grid/local refinement algorithm for both two- and three-dimensional flows are presented.