36 citations · 37 across the 5 of their papers we have counts for
5 papers
On the TVD property of second order methods for 2D scalar conservation laws
Lilia Krivodonova, Alexey Smirnov
The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation l…
Three-dimensional simulations of sound propagation in a trumpet with accurate mouthpiece shank geometry
Janelle Resch, Lilia Krivodonova, John Vanderkooy
The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finite-amplitude wav…
Discontinuous Galerkin methods on graphics processing units for nonlinear hyperbolic conservation laws
Martin Fuhry, Andrew Giuliani, Lilia Krivodonova
We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDI…
Edge coloring in unstructured CFD codes
Andrew Giuliani, Lilia Krivodonova
We propose a way of preventing race conditions in the evaluation of the surface integral contribution in discontinuous Galerkin and finite volume flow solvers by coloring the edges…
Spatial and Modal Superconvergence of the Discontinuous Galerkin Method for Linear Equations
Noel Chalmers, Lilia Krivodonova
We apply the discontinuous Galerkin finite element method with a degree polynomial basis to the linear advection equation and derive a PDE which the numerical solution solves e…