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Partial and Spectral-Viscosity Models for Geophysical Flows

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Chinese Annals of Mathematics,Series B 2010年第5期31卷 579-606页

作者： Qingshan CHEN max gunzburger Xiaoming WANG Department of Scientific Computing Florida State University Tallahassee FL 32306 USA. Department of Mathematics. FloridaState University Tallahassee FL 32306 USA.

Two models based on the hydrostatic primitive equations are *** first model is the primitive equations with partial viscosity only,and is oriented towards large-scale wave structures in the ocean and *** second model is the viscous primitive equations with spectral eddy viscosity,and is oriented towards turbulent geophysical *** both models,the existence and uniqueness of global strong solutions are *** the second model,the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established.

关键词： Primitive equations Partial viscosity Spectral-eddy viscosity

Bridging Methods for Atomistic-to-Continuum Coupling and Their Implementation

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Communications in Computational Physics 2010年第4期7卷 831-876页

作者： Pablo Seleson max gunzburger Department of Scientific Computing Florida State UniversityTallahasseeFL 32306-4120USA

Several issues connected with bridging methods for atomistic-to-continuum(AtC)coupling are *** coupling approaches using various energy blending models are studied as well as the influence that model parameters,blending functions,and grids have on simulation *** use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge *** also show that continuum models are not appropriate for dealing with problems with singular loads,whereas AtC bridging methods yield correct results,thus justifying the need for a multiscale *** investigate models that involve multiple-neighbor interactions in the atomistic region,particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.

关键词： Multiscale modeling atomistic-to-continuum coupling boundary treatment

Advances in Studies and Applications of Centroidal Voronoi Tessellations

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Numerical Mathematics(Theory,Methods and Applications) 2010年第2期3卷 119-142页

作者： Qiang Du max gunzburger Lili Ju Department of Mathematics Pennsylvania State University University Park PA16802 USA. Department of Scientific Computing Florida State University Tallahassee FL32306 USA. Department of Mathematics University of South Carolina Columbia SC29208USA.

Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known *** then present an overview of recent advances in both mathematical and computational studies and in practical applications of *** possible,we point out some outstanding issues that still need investigating.

关键词： Voronoi tessellations centroids clustering mesh generation and optimization imageprocessing model reduction point sampling.

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

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Communications in Computational Physics 2009年第9期6卷 673-698页

作者： Sangbum Kim max gunzburger Janet Peterson Chia-Ren Hu Division of Energy Systems Research Ajou UniversitySuwon 442-749Korea Department of Scientific Computing Florida State UniversityTallahasseeFL 32309-4120USA Center for Theoretical Physics Department of PhysicsTexas A&M UniversityCollege StationTexas 77843USA

A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is *** computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes,aspect ratios,and crosssectional shapes,i.e.,squares,triangles,circles,pentagons,and four star *** vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s)of the *** eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each ***-antivortex(V-AV)configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational *** V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase *** are made between the results obtained for the different sample shapes.

关键词： Superconductivity nucleation symmetry finite element method

Peridynamic State-Based Models and the Embedded-Atom Model

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Communications in Computational Physics 2014年第1期15卷 179-205页

作者： Pablo Seleson Michael L.Parks max gunzburger Institute for Computational Engineering and Sciences 201 East 24th StStop C0200AustinTexas 78712-1229USA. Sandia National Laboratories Computing Research CenterP.O.Box 5800MS 1320AlbuquerqueNM 87185-1320USA. Department of Scientific Computing 400 Dirac Science LibraryFlorida State UniversityTallahasseeFL 32306-4120USA.

We investigate connections between nonlocal continuum models and molecular dynamics.A continuous upscaling of molecular dynamics models of the form of the embedded-atom model is presented,providing means for simulating molecular dynamics systems at greatly reduced *** are presented for structured and structureless material models,supported by computational *** nonlocal continuum models are shown to be instances of the state-based peridynamics *** relating multibody peridynamic models and upscaled nonlocal continuum models are derived.

关键词： Peridynamics multibody potentials embedded-atom molecular dynamics.

A Parallel Computational Model for Three-Dimensional,Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

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Communications in Computational Physics 2014年第9期16卷 1056-1080页

作者： Wei Leng Lili Ju max gunzburger Stephen Price State Key Laboratory of Scientific and Engineering Computing Chinese Academy of SciencesBeijing 100190China. Department of Mathematics University of South CarolinaColumbiaSC 29208USA. Department of Scientific Computing Florida State UniversityTallahasseeFL 32306USA. Theoretical Division Los Alamos National LaboratoryLos AlamosNM 87545.USA.

This paper focuses on the development of an efficient,three-dimensional,thermo-mechanical,nonlinear-Stokes flow computational model for ice sheet *** model is based on the parallel finite element model developed in[14]which features high-order accurate finite element discretizations on variable resolution ***,we add an improved iterative solution method for treating the nonlinearity of the Stokes problem,a new high-order accurate finite element solver for the temperature equation,and a new conservative finite volume solver for handling mass *** result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet *** demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland *** also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured ***,we find no evidence for the“cold spoke”instabilities observed for these same experiments when using finite difference,shallow-ice approximation models on structured grids.

关键词： Stokes-flow modeling ice-sheet modeling finite element approximation finite volume approximation parallel implementation.

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

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Numerical Mathematics(Theory,Methods and Applications) 2011年第3期4卷 396-418页

作者： Huai Zhang Lili Ju max gunzburger Todd Ringler Stephen Price Department of Mathematics University of South CarolinaColumbiaSC 29208USA. Department of Scientific Computing Florida State UniversityTallahasseeFL 32306USA. Theoretical Division Los Alamos National LaboratoryLos AlamosNM 87545USA. Laboratory of Computational Geodynamics Graduate University of Chinese Academy of SciencesBeijing100049China.

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice *** governing thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness ***,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model *** solvers are integrated through a well-designed coupler for the exchange of parametric data between com*** discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel *** demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.

关键词： Ice sheet modeling nonlinear Stokes equation finite element method parallel implementation centroial Voronoi Delaunay meshes.

A Second-Order Implicit-Explicit Scheme for the Baroclinic-Barotropic Split System of Primitive Equations

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Communications in Computational Physics 2023年第10期34卷 1306-1331页

作者： Rihui Lan Lili Ju Zhu Wang max gunzburger School of Mathematical Sciences Ocean University of ChinaQingdaoShandong 266100China Department of Mathematics University of South CarolinaColumbiaSC 29208USA Oden Institute for Computational Engineering and Sciences University of Texas at AustinAustinTexas 78712USA

The baroclinic-barotropic mode splitting technique is commonly employed in numerical solutions of the primitive equations for ocean modeling to deal with the multiple time scales of ocean *** this paper,a second-order implicit-explicit(IMEX)scheme is proposed to advance the baroclinic-barotropic split ***,the baroclinic mode and the layer thickness of fluid are evolved explicitly via the second-order strong stability preserving Runge-Kutta scheme,while the barotropic mode is advanced implicitly using the linearized Crank-Nicolson *** each time step,the baroclinic velocity is first computed using an intermediate barotropic *** barotropic velocity is then corrected by re-advancing the barotropic mode with an improved barotropic ***,the layer thickness is updated by coupling the baroclinic and barotropic velocities *** addition,numerical inconsistencies on the discretized sea surface height caused by the mode splitting are alleviated via a reconciliation process with carefully calculated flux *** truncation error is also analyzed to validate the second-order accuracy of the ***,two benchmark tests from the MPAS-Ocean platform are conducted to numerically demonstrate the performance of the proposed IMEX scheme.

关键词： Primitive equations baroclinic-barotropic splitting implicit-explicit strong stability preserving RK SSH reconciliation

Meshfree First-order System Least Squares

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Numerical Mathematics(Theory,Methods and Applications) 2008年第1期1卷 29-43页

作者： Hugh R.MacMillan max D.gunzburger John V.Burkardt Department of Mathematical Sciences Clemson University ClemsonSC 29634-0975USA. School of Computational Science Florida State University TallahasseeFL 32306-4120USA. Advanced Research Computing Virginia Tech University BlacksburgVA 24061-0123USA.

We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- *** numerical results are provided and remaining challenges are discussed.

关键词： Meshfree methods first-order system least squares adaptive finite elements