5 citations · 9 across the 8 of their papers we have counts for
9 papers
Two-Dimensional Shallow Water Linearized Moment Equations: Hyperbolicity and Well-Balanced Schemes
Shiping Zhou, Juntao Huang, Andrew Christlieb
We study rotational invariance, hyperbolicity, and well-balanced discretization of shallow water linearized moment equations in two horizontal dimensions. Although the direct exten…
Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods
César Herrera, John Driscoll, Sigal Gottlieb +3
Mixed precision Runge--Kutta methods reduce the cost of the expensive implicit solves in diagonally implicit Runge--Kutta (DIRK) schemes by evaluating them in low precision, while…
A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System
Mandela B. Quashie, J. W. Burby, Andrew J. Christlieb +1
We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-ce…
A Semi-Lagrangian Adaptive Rank (SLAR) Method for High-Dimensional Vlasov Dynamics
Nanyi Zheng, William A. Sands, Daniel Hayes +2
We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order…
Moment-enhanced shallow-water equations with an effective wall closure for no-slip bottoms
Shiping Zhou, Juntao Huang, Andrew J. Christlieb
Shallow-water equations and low-order shallow-water moment models use vertically coarse representations and therefore cannot, in general, resolve the thin wall-affected region prod…
A Particle-In-Cell Method for Plasmas with a Generalized Momentum Formulation, Part III: A Family of Gauge Conserving Methods
Andrew J. Christlieb, William A. Sands, Stephen R. White
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell's equations under…
A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition
Andrew J. Christlieb, William A. Sands, Stephen White
In a previous paper, we developed a new particle-in-cell method for the Vlasov-Maxwell system in which the electromagnetic fields and the equations of motion for the particles were…
Hyperbolic Machine Learning Moment Closures for the BGK Equations
Andrew J. Christlieb, Mingchang Ding, Juntao Huang +1
We introduce a hyperbolic closure for the Grad moment expansion of the Bhatnagar-Gross-Krook's (BGK) kinetic model using a neural network (NN) trained on BGK's moment data. This cl…
The Picard integral formulation of weighted essentially non-oscillatory schemes
David C. Seal, Yaman Güçlü, Andrew J. Christlieb
High-order temporal discretizations for hyperbolic conservation laws have historically been formulated as either a method of lines (MOL) or a Lax-Wendroff method. In the MOL viewpo…