D. Graves - Academia.edu (original) (raw)

Papers by D. Graves

Research paper thumbnail of Barad, M., P. Colella, D. Graves, B. VanStraalen, "An adaptive Cartesian grid embedded bound- ary method for the incompressible Navier-Stokes equations" In preparation for the Journal of Computational Physics

Research paper thumbnail of Chombo software package for amr applications

Research paper thumbnail of A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions

Journal of Computational Physics, 2008

We present a method for computing incompressible viscous flows in three dimensions using blockstr... more We present a method for computing incompressible viscous flows in three dimensions using blockstructured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time. We use an L_0-stable second-order semi-implicit scheme to evaluate the viscous terms. Results are presented to demonstrate the accuracy and effectiveness of this approach.

Research paper thumbnail of EBChombo Software Package for Cartesian Grid

Research paper thumbnail of Petascale Block-Structured AMR Applications without Distributed Meta-data

Adaptive mesh refinement (AMR) applications to solve partial differential equations (PDE) are ver... more Adaptive mesh refinement (AMR) applications to solve partial differential equations (PDE) are very challenging to scale efficiently to the petascale regime. We describe optimizations to the Chombo AMR framework that enable it to scale efficiently to petascale on the Cray XT5. We describe an example of a hyperbolic solver (inviscid gas dynamics) and an matrix-free geometric multigrid elliptic solver. Both show good weak scaling to 131K processors without any thread-level or SIMD vector parallelism. This paper describes the algorithms used to compress the Chombo metadata and the optimizations of the Chombo infrastructure that are necessary for this scaling result. That we are able to achieve petascale performance without distribution of the metadata is a significant advance which allows for much simpler and faster AMR codes.

Research paper thumbnail of An efficient solver for the equations of resistive MHD with spatially-varying resistivity

Journal of Computational Physics, 2008

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizat... more We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discretizations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficient solvers.

Research paper thumbnail of AMR Godunov Unsplit Algorithm and Implementation

Research paper thumbnail of Chombo Software Package for AMR Applications-Design Document

Applied Numerical …

This document was prepared as an account of work sponsored by the United States Government. While... more This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of ...

Research paper thumbnail of EBAMRTools: EBChombo's Adaptive Reflnement Library

Research paper thumbnail of A tightly coupled particle-fluid model for DNA-laden flows in complex microscale geometries

We present a stable and convergent method for the computation of flows of DNA-laden fluids in mic... more We present a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry. The numerical strategy combines a ball-rod model representation for polymers coupled tightly with a projection method for incompressible viscous flow. We use Cartesian grid embedded boundary methods to discretize the fluid equations in the presence of complex domain boundaries. A sample calculation is presented showing flow through a packed array microchannel in two dimensions.

Research paper thumbnail of A Cartesian grid embedded boundary method for hyperbolic conservation laws

Journal of Computational Physics, 2006

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conserv... more 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 smallcell 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.

Research paper thumbnail of EBChombo Software Package for Cartesian Grid, Embedded Boundary Applications

Research paper thumbnail of A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics, 2011

We present a method for solving Poisson and heat equations with discontinuous coefficients in two... more We present a method for solving Poisson and heat equations with discontinuous coefficients in two-and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in . Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10 6 , thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

Research paper thumbnail of Embedded Boundary AMR Elliptic Algorithm and Implementation

Research paper thumbnail of A Cartesian grid embedded boundary method for incompressible flow

Research paper thumbnail of A higher-order upwind method for viscoelastic flow

Communications in Applied Mathematics and Computational Science, 2009

We present a conservative finite difference method designed to capture elastic wave propagation i... more We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier-Stokes equations with an extra viscoelastic stress described by the Oldroyd-B constitutive equations. The equations are cast into a hybrid conservation form which is amenable to the use of a second-order Godunov method for the hyperbolic part of the equations, including a new exact Riemann solver. A numerical stress splitting technique provides a well-posed discretization for the entire range of Newtonian and elastic fluids. Incompressibility is enforced through a projection method and a partitioning of variables that suppresses compressive waves. Irregular geometry is treated with an embedded boundary/volume-of-fluid approach. The method is stable for time steps governed by the advective Courant-Friedrichs-Lewy (CFL) condition. We present second-order convergence results in L 1 for a range of Oldroyd-B fluids.

Research paper thumbnail of Short Note An efficient solver for the equations of resistive MHD with spatially-varying resistivity

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizat... more We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discret- izations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficient solvers. 2008 Published by Elsevier Inc.

Research paper thumbnail of A Cartesian Grid Embedded Boundary Method for the Compressible Navier-Stokes Equations

Communications in Applied Mathematics and Computational Science, 2013

ABSTRACT We present an unsplit method for the time-dependent compressible Navier-Stokes equations... more ABSTRACT We present an unsplit method for the time-dependent compressible Navier-Stokes equations in two and three dimensions. We use a conservative, second-order Godunov algorithm. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We solve for viscous and conductive terms with a second-order semiimplicit algorithm. We demonstrate second-order accuracy in solutions of smooth problems in smooth geometries and demonstrate robust behavior for strongly discontinuous initial conditions in complex geometries.

Research paper thumbnail of A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics, 2011

We present a method for solving Poisson and heat equations with discontinuous coefficients in two... more We present a method for solving Poisson and heat equations with discontinuous coefficients in two-and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in . Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10 6 , thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

Research paper thumbnail of A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries

We present a stable and convergent method for the computation of flows of DNA-laden fluids in mic... more We present a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry. The numerical strategy combines a ball-rod model representation for polymers coupled tightly with a projection method for incompressible viscous flow. We use Cartesian grid embedded boundary methods to discretize the fluid equations in the presence of complex domain boundaries. A sample calculation is presented showing flow through a packed array microchannel in two dimensions.

Research paper thumbnail of Barad, M., P. Colella, D. Graves, B. VanStraalen, "An adaptive Cartesian grid embedded bound- ary method for the incompressible Navier-Stokes equations" In preparation for the Journal of Computational Physics

Research paper thumbnail of Chombo software package for amr applications

Research paper thumbnail of A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions

Journal of Computational Physics, 2008

We present a method for computing incompressible viscous flows in three dimensions using blockstr... more We present a method for computing incompressible viscous flows in three dimensions using blockstructured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time. We use an L_0-stable second-order semi-implicit scheme to evaluate the viscous terms. Results are presented to demonstrate the accuracy and effectiveness of this approach.

Research paper thumbnail of EBChombo Software Package for Cartesian Grid

Research paper thumbnail of Petascale Block-Structured AMR Applications without Distributed Meta-data

Adaptive mesh refinement (AMR) applications to solve partial differential equations (PDE) are ver... more Adaptive mesh refinement (AMR) applications to solve partial differential equations (PDE) are very challenging to scale efficiently to the petascale regime. We describe optimizations to the Chombo AMR framework that enable it to scale efficiently to petascale on the Cray XT5. We describe an example of a hyperbolic solver (inviscid gas dynamics) and an matrix-free geometric multigrid elliptic solver. Both show good weak scaling to 131K processors without any thread-level or SIMD vector parallelism. This paper describes the algorithms used to compress the Chombo metadata and the optimizations of the Chombo infrastructure that are necessary for this scaling result. That we are able to achieve petascale performance without distribution of the metadata is a significant advance which allows for much simpler and faster AMR codes.

Research paper thumbnail of An efficient solver for the equations of resistive MHD with spatially-varying resistivity

Journal of Computational Physics, 2008

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizat... more We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discretizations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficient solvers.

Research paper thumbnail of AMR Godunov Unsplit Algorithm and Implementation

Research paper thumbnail of Chombo Software Package for AMR Applications-Design Document

Applied Numerical …

This document was prepared as an account of work sponsored by the United States Government. While... more This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of ...

Research paper thumbnail of EBAMRTools: EBChombo's Adaptive Reflnement Library

Research paper thumbnail of A tightly coupled particle-fluid model for DNA-laden flows in complex microscale geometries

We present a stable and convergent method for the computation of flows of DNA-laden fluids in mic... more We present a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry. The numerical strategy combines a ball-rod model representation for polymers coupled tightly with a projection method for incompressible viscous flow. We use Cartesian grid embedded boundary methods to discretize the fluid equations in the presence of complex domain boundaries. A sample calculation is presented showing flow through a packed array microchannel in two dimensions.

Research paper thumbnail of A Cartesian grid embedded boundary method for hyperbolic conservation laws

Journal of Computational Physics, 2006

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conserv... more 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 smallcell 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.

Research paper thumbnail of EBChombo Software Package for Cartesian Grid, Embedded Boundary Applications

Research paper thumbnail of A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics, 2011

We present a method for solving Poisson and heat equations with discontinuous coefficients in two... more We present a method for solving Poisson and heat equations with discontinuous coefficients in two-and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in . Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10 6 , thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

Research paper thumbnail of Embedded Boundary AMR Elliptic Algorithm and Implementation

Research paper thumbnail of A Cartesian grid embedded boundary method for incompressible flow

Research paper thumbnail of A higher-order upwind method for viscoelastic flow

Communications in Applied Mathematics and Computational Science, 2009

We present a conservative finite difference method designed to capture elastic wave propagation i... more We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier-Stokes equations with an extra viscoelastic stress described by the Oldroyd-B constitutive equations. The equations are cast into a hybrid conservation form which is amenable to the use of a second-order Godunov method for the hyperbolic part of the equations, including a new exact Riemann solver. A numerical stress splitting technique provides a well-posed discretization for the entire range of Newtonian and elastic fluids. Incompressibility is enforced through a projection method and a partitioning of variables that suppresses compressive waves. Irregular geometry is treated with an embedded boundary/volume-of-fluid approach. The method is stable for time steps governed by the advective Courant-Friedrichs-Lewy (CFL) condition. We present second-order convergence results in L 1 for a range of Oldroyd-B fluids.

Research paper thumbnail of Short Note An efficient solver for the equations of resistive MHD with spatially-varying resistivity

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizat... more We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discret- izations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficient solvers. 2008 Published by Elsevier Inc.

Research paper thumbnail of A Cartesian Grid Embedded Boundary Method for the Compressible Navier-Stokes Equations

Communications in Applied Mathematics and Computational Science, 2013

ABSTRACT We present an unsplit method for the time-dependent compressible Navier-Stokes equations... more ABSTRACT We present an unsplit method for the time-dependent compressible Navier-Stokes equations in two and three dimensions. We use a conservative, second-order Godunov algorithm. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We solve for viscous and conductive terms with a second-order semiimplicit algorithm. We demonstrate second-order accuracy in solutions of smooth problems in smooth geometries and demonstrate robust behavior for strongly discontinuous initial conditions in complex geometries.

Research paper thumbnail of A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics, 2011

We present a method for solving Poisson and heat equations with discontinuous coefficients in two... more We present a method for solving Poisson and heat equations with discontinuous coefficients in two-and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in . Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10 6 , thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

Research paper thumbnail of A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries

We present a stable and convergent method for the computation of flows of DNA-laden fluids in mic... more We present a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry. The numerical strategy combines a ball-rod model representation for polymers coupled tightly with a projection method for incompressible viscous flow. We use Cartesian grid embedded boundary methods to discretize the fluid equations in the presence of complex domain boundaries. A sample calculation is presented showing flow through a packed array microchannel in two dimensions.