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AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Davis, Andrew Guzik, Stephen Gao, Xinfeng Computational Fluid Dynamics and Propulsion Laboratory University of Virginia CharlottesvilleVA22904 United States Applied Numerical Algorithms Group Lawrence Berkely National Lab BerkelyCA94720 United States

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

The performance of a brick-based and hash-table-based framework, HashBrick, supporting distributed structured-grid calculations on heterogeneous architectures, is evaluated with a fourth-order accurate finite-volume algorithm in space and time. HashBrick is implemented with brick data structures and hash tables to provide performance portability across CPUs and GPUsondistributed parallel architectures. It is optimized for CFD algorithms characterized by local clusters of structured-grid data that are otherwise sparsely distributed in the domain. Asimple acoustic Gaussian pulse problem is solved to primarily stress memory bandwidth and latency. A weak-scaling study was performed to demonstrate HashBrick’s performance on multiple computing nodes. The performance of HashBrick is assessed by comparing wall-clock time and energy against a CPU-only CFD solver, for the same power budget. Two-sided MPI communication with a bulk synchronization is compared against one-sided SHMEM and NVSHMEMcommunication. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Brick

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Optimization of a Triangular Delaunay Mesh Generator using Reinforcement Learning

arXiv

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arXiv 2025年

作者： Thacher, Will Pan, Yulong Persson, Per-Olof Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Applied Science and Technology Group University of California Berkeley BerkeleyCA94720 United States Mathematics Group Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics University of California Berkeley BerkeleyCA94720 United States

In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies vertices, and a standard Delaunay algorithm to triangulate the vertices. We explore various design choices and evaluate our mesh generator on various tasks including mesh generation, mesh improvement, and producing variable resolution meshes. The learned mesh generator outputs meshes that are comparable to those produced by Triangle and DistMesh, two popular Delaunay-based mesh generators. © 2025, CC BY.

关键词： Reinforcement learning

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A freestream-preserving high-order finite-volume method for mapped grids with adaptive-mesh refinement 50

A freestream-preserving high-order finite-volume method for ...

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50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

作者： Guzik, Stephen M. McCorquodale, Peter Colella, Phillip Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA 94551 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory Berkeley CA 94720 United States

ISBN: (数字)9781600869365

A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). Advancement in time is achieved with a fourth-order Runge-Kutta method.

关键词： Finite volume method

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Steady-state solution-adaptive euler computations on structured grids 36th

Steady-state solution-adaptive euler computations on structu...

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36th AIAA Aerospace Sciences Meeting and Exhibit, 1998

作者： Dudek, Scott A. Colella, Phillip Numerical Modeling Section McDermott Technology Inc AllianceOH United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Mechanical Engineering The University of California Berkeley United States

A local solution-adaptive mesh refinement algorithm is used to produce steady-state flow results on structured grids for the two-dimensional Euler equations. The solution is marched to steady state using an explicit, cell-centered, second-order unsplit multidimensional upwind method. Convergence is accelerated by local time stepping and a multigrid method. The flexibility and efficiency of the algorithm are shown by presenting three test cases, a variety of subsonic and transonic internal and external flows. © 1998 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

关键词： Computational fluid dynamics

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Continuum kinetic model for simulating low-collisionality regimes in plasmas

Continuum kinetic model for simulating low-collisionality re...

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2013 19th IEEE Pulsed Power Conference, PPC 2013

作者： Vogman, G.V. Colella, P. Applied Science and Technology Program University of California - Berkeley Berkeley CA 94704 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley CA 94720 United States

ISBN: (纸本)9781467351676

Continuum kinetic models, such as Maxwell-Boltzmann, present a viable alternative to particle-in-cell (PIC) models because they can be cast in conservation form and are not susceptible to noise. By treating the associated phase space distribution function as a continuous incompressible fluid occupying a volume of position-velocity space, evolution of the distribution function is determined by solving a 6-D advection equation. In cases where collision terms are negligible, the Boltzmann model is reduced to a Vlasov model. A 4th-order accurate continuum kinetic Vlasov model has been developed in one spatial and one velocity dimension to address the challenges associated with solving a hyperbolic governing equation in multidimensional phase space. The governing equation is cast in conservation law form and solved with a finite volume representation. Adaptive mesh refinement (AMR) is used to allow for efficient use of computational resources while maintaining desired levels of resolution. Consequently, with AMR the model is able to capture the fine structures that develop in the distribution function as it evolves in time, while using low resolution in the tail of the distribution function. The model is tested on several plasma phenomena including: weak and strong Landau damping and the two-stream instability. Conservation properties of the method are investigated. © 2013 IEEE.

关键词： Distribution functions

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SCALLOP: A highly scalable parallel poisson solver in three dimensions 03

SCALLOP: A highly scalable parallel poisson solver in three ...

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2003 ACM/IEEE Conference on Supercomputing, SC 2003

作者： Balls, Gregory T. Baden, Scott B. Colella, Phillip Department of Computer Science and Engineering University of California San Diego 9500 Gilman Drive San Diego CA 92093-0114 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory Berkeley CA United States

ISBN: (纸本)1581136951

SCALLOP is a highly scalable solver and library for elliptic partial differential equations on regular block-structured domains. SCALLOP avoids high communication overheads algorithmically by taking advantage of the locality properties inherent to solutions to elliptic PDEs. Communication costs are small, on the order of a few percent of the total running time on up to 1024 processors of NPACI's and NERSC's IBM Power-3 SP sytems. SCALLOP trades off numerical overheads against communication. These numerical overheads are independent of the number of processors for a wide range of problem sizes. SCALLOP is implicitly designed for infinite domain (free space) boundary conditions, but the algorithm can be reformulated to accommodate other boundary conditions. The SCALLOP library is built on top of the KeLP programming system and runs on a variety of platforms. © 2003 ACM.

关键词： Boundary conditions

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Polymer simulation for single molecule detection in microdevices

Polymer simulation for single molecule detection in microdev...

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作者： Kallemov, B. Miller, G.H. Trebotich, D. University of California Davis CA 95616 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory MS 50A-1148 1 Cyclotron Road Berkeley CA 94720 United States

ISBN: (纸本)9781439834022

We have developed a novel algorithm for the simulation of polymer-laden flows in microfluidic devices. Our algorithm is based on a hybridization of high-order accurate continuum and particle methods. The continuum algorithm provides the basic framework for high performance computations to resolve device length and time scales. It is coupled to a new particle method with an optimized treatment of particle interactions such that the time step is on the level of the fluid continuum. We demonstrate our simulation capability on the flow of DNA molecules in a contraction microchannel used for single molecule detection.

关键词： Microfluidics

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A tightly coupled particle-fluid model for DNA-laden flows in complex microscale geometries

A tightly coupled particle-fluid model for DNA-laden flows i...

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3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

作者： Trebotich, D. Miller, G.H. Colellac, P. Graves, D.T. Martin, D.F. Schwartz, P.O. Lawrence Livermore National Laboratory Center for Applied Scientific Computing PO Box 808 L-560 Livermore CA 94551 United States Department of Applied Science University of California One Shields Avenue Davis CA 95616 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley CA 94720 United States

ISBN: (纸本)0080444814

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. © 2005 Elsevier Ltd.

关键词： Microfluidics

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A High Order Cartesian Grid, Finite Volume Method for Elliptic Interface Problems

SSRN

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SSRN 2023年

作者： Thacher, Will Johansen, Hans Martin, Daniel Applied Science and Technology Group University of California Berkeley BerkeleyCA94720 United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced. © 2023, The Authors. All rights reserved.

关键词： Finite volume method

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A High Order Cartesian Grid, Finite Volume Method for Elliptic Interface Problems

arXiv

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arXiv 2023年

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green’s theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced. © 2023, CC BY.

关键词： Finite volume method

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