12 papers
Adaptive, efficient, and scalable water wave modeling with dispersive hyperbolic systems
Carlos Muñoz-Moncayo, David I. Ketcheson
Accurate modeling of tsunamis (such as those generated by landslides) requires capturing both wave dispersion in the deep ocean and wave breaking near the shore. The shallow water…
Solitary wave formation in the compressible Euler equations
David I. Ketcheson, Giovanni Russo
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We sho…
Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
Hendrik Ranocha, David I. Ketcheson
We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of…
Homogenized Equations for Isentropic Gas in a Pipe with Periodically-Varying Cross-Section
Laila S. Busaleh, David I. Ketcheson
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effect…
Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations
Manvendra Pratap Rajvanshi, David I. Ketcheson
We study relaxation-based approaches for conserving mass and energy in the numerical solution of Schrödinger-Poisson (SP) type systems. Relaxation-based methods offer a general ap…
Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson +2
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods…