194 citations · 454 across the 22 of their papers we have counts for
25 papers
Positivity-preserving semi-Lagrangian discontinuous Galerkin methods for multi-species Vlasov-Ampère models of plasma
Dauda Gambo, James A. Rossmanith
We develop a high-order and positivity-preserving kinetic solver for the multi-species Vlasov-Ampère system that is built within a semi-Lagrangian discontinuous Galerkin (SLDG) fra…
Micro-macro kinetic flux-vector splitting schemes for the multidimensional Boltzmann-ES-BGK equation
James A. Rossmanith, Preeti Sar
The kinetic Boltzmann equation models gas dynamics over a wide range of spatial and temporal scales. Simplified versions of the full Boltzmann collision operator, such as the class…
A novel splitting method for Vlasov-Ampere
James A. Rossmanith, Christine Vaughan
Vlasov equations model the dynamics of plasma in the collisionless regime. A standard approach for numerically solving the Vlasov equation is to operator split the spatial and velo…
Positivity-Preserving Lax-Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models
Erica R. Johnson, James A. Rossmanith, Christine Vaughan
The quadrature-based method of moments (QMOM) offers a promising class of approximation techniques for reducing kinetic equations to fluid equations that are valid beyond thermodyn…
A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
Makrand A. Khanwale, Kumar Saurabh, Masado Ishii +3
The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In t…
Parallel Scaling of the Regionally-Implicit Discontinuous Galerkin Method with Quasi-Quadrature-Free Matrix Assembly
Andrew J. Christlieb, Pierson T. Guthrey, James A. Rossmanith
In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving t…
Semi-implicit Hybrid Discrete Approximation of Thermal Radiative Transfer
Ryan G. McClarren, James A. Rossmanith, Minwoo Shin
The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and ef…
A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes
Makrand A Khanwale, Kumar Saurabh, Milinda Fernando +4
We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we e…
Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes
Makrand A Khanwale, Alec D. Lofquist, Hari Sundar +2
We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An…
A Positivity-Preserving Limiting Strategy for Locally-Implicit Lax-Wendroff Discontinuous Galerkin Methods
Camille Felton, Mariana Harris, Caleb Logemann +3
Nonlinear hyperbolic conservation laws admit singular solutions such as shockwaves (discontinuities in conserved variables), rarefaction waves (discontinuities in derivatives), and…
The Regionally-Implicit Discontinuous Galerkin Method: Improving the Stability of DG-FEM
Pierson T. Guthrey, James A. Rossmanith
Discontinuous Galerkin (DG) methods for hyperbolic partial differential equations (PDEs) with explicit time-stepping schemes, such as strong stability-preserving Runge-Kutta (SSP-R…
Positivity-preserving discontinuous Galerkin methods with Lax-Wendroff time discretizations
Scott A. Moe, James A. Rossmanith, David C. Seal
This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivity-preserving and can be applied on both Cartesian and unstruc…
A Simple and Effective High-Order Shock-Capturing Limiter for Discontinuous Galerkin Methods
Scott A. Moe, James A. Rossmanith, David C. Seal
The discontinuous Galerkin (DG) finite element method when applied to hyperbolic conservation laws requires the use of shock-capturing limiters in order to suppress unphysical osci…
High-Order Discontinuous Galerkin Finite Element Methods with Globally Divergence-Free Constrained Transport for Ideal MHD
James A. Rossmanith
The modification of the celebrated Yee scheme from Maxwell equations to magnetohydrodynamics is often referred to as the constrained transport approach. Constrained transport can b…
Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics
Andrew J. Christlieb, James A. Rossmanith, Qi Tang
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in…
Outflow Positivity Limiting for Hyperbolic Conservation Laws. Part I: Framework and Recipe
Evan Alexander Johnson, James A. Rossmanith
Numerical methods for hyperbolic conservation laws are needed that efficiently mimic the constraints satisfied by exact solutions, including material conservation and positivity, w…
A Class of Quadrature-Based Moment-Closure Methods with Application to the Vlasov-Poisson-Fokker-Planck System in the High-Field Limit
Yongtao Cheng, James A. Rossmanith
Quadrature-based moment-closure methods are a class of approximations that replace high-dimensional kinetic descriptions with lower-dimensional fluid models. In this work we invest…
A high-order unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations based on the method of lines
Christiane Helzel, James A. Rossmanith, Bertram Taetz
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete diver…
A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
J. A. Rossmanith, D. C. Seal
The Vlasov-Poisson equations describe the evolution of a collisionless plasma, represented through a probability density function (PDF) that self-interacts via an electrostatic for…
Ten-moment two-fluid plasma model agrees well with PIC/Vlasov in GEM problem
E. Alec Johnson, James A. Rossmanith
We simulate magnetic reconnection in the GEM problem using a two-fluid model with 10 moments for the electron fluid as well as the proton fluid. We show that use of 10 moments for…
Simulation of Fast Magnetic Reconnection using a Two-Fluid Model of Collisionless Pair Plasma without Anomalous Resistivity
E. Alec Johnson, James A. Rossmanith
For the first time to our knowledge, we demonstrate fast magnetic reconnection near a magnetic null point in a fluid model of collisionless pair plasma without resorting to the con…
An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
Christiane Helzel, James A. Rossmanith, Bertram Taetz
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discret…
Collisionless Magnetic Reconnection in a Five-Moment Two-Fluid Electron-Positron Plasma
E. A. Johnson, J. A. Rossmanith
We simulate magnetic reconnection in electron-positron (pair) plasma using a collisionless two-fluid model with isotropic pressure. In this model the resistive, Hall, and electroki…
A class of residual distribution schemes and their relation to relaxation systems
James A. Rossmanith
Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinel…