134 citations · 1.1k across the 79 of their papers we have counts for
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Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation
Abhijit Biswas, David I. Ketcheson, Hendrik Ranocha +1
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of so…
Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form
Hendrik Ranocha, Mario Ricchiuto
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requi…
Pseudo-Energy-Preserving Explicit Runge-Kutta Methods
Gabriel A. Barrios de León, David I. Ketcheson, Hendrik Ranocha
Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Ha…
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters +3
High-order numerical methods for conservation laws are highly sought after due to their potential efficiency. However, it is challenging to ensure their robustness, particularly fo…
Structure-Preserving Numerical Methods for Fokker-Planck Equations
Hanna Bartel, Joshua Lampert, Hendrik Ranocha
A common way to numerically solve Fokker-Planck equations is the Chang-Cooper method in space combined with one of the Euler methods in time. However, the explicit Euler method is…
Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
Joshua Lampert, Hendrik Ranocha
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of d…