P. McCorquodale

Bio: P. McCorquodale is an academic researcher from Lawrence Berkeley National Laboratory. The author has contributed to research in topics: Adaptive mesh refinement & Finite volume method. The author has an hindex of 16, co-authored 36 publications receiving 1139 citations.

Chombo Software Package for AMR Applications Design Document

Abstract: Chombo Software Package for AMR Applications Design Document M. Adams P. Colella D. T. Graves J. N. Johnson H. S. Johansen N. D. Keen T. J. Ligocki D. F. Martin P. W. McCorquodale D. Modiano P. O. Schwartz T. D. Sternberg B. Van Straalen Applied Numerical Algorithms Group Computational Research Division Lawrence Berkeley National Laboratory Berkeley, CA February 27, 2014

A high-order finite-volume method for conservation laws on locally refined grids

Abstract: We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that developed by Colella, Dorr, Hittinger and Martin (2009) to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge–Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge–Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter of Colella and Sekora (2008), as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

Abstract: Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations, and present examples of application in Heavy Ion Fusion and related fields which illustrate the effectiveness of the approach. We also report on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG's mesh refinement library Chombo to include the tools needed by Particle-In-Cell simulation codes.

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

Abstract: Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. A brief discussion of the challenges posed by coupling this technique with plasma particle-in-cell simulations is given, followed by a presentation of examples of application in heavy ion fusion and related fields which illustrate the effectiveness of the approach. Finally, a report is given on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG’s mesh refinement library Chombo to include the tools needed by particle-in-cell simulation codes.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

Abstract: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.