138 citations · 481 across the 13 of their papers we have counts for
4 papers · 1 filter
CFL Optimized Forward-Backward Runge-Kutta Schemes for the Shallow Water Equations
Jeremy R. Lilly, Darren Engwirda, Giacomo Capodaglio +2
We present the formulation and optimization of a Runge-Kutta-type time-stepping scheme for solving the shallow water equations, aimed at substantially increasing the effective allo…
Local time stepping for the shallow water equations in MPAS
Giacomo Capodaglio, Mark Petersen
We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LT…
On the Spatial and Temporal Order of Convergence of Hyperbolic PDEs
Siddhartha Bishnu, Mark Petersen, Bryan Quaife
In this work, we determine the full expression for the global truncation error of hyperbolic partial differential equations (PDEs). In particular, we use theoretical analysis and s…
Tracer Transport within an Unstructured Grid Ocean Model using Characteristic Discontinuous Galerkin Advection
D. Lee, M. Petersen, R. Lowrie +1
In a previous article a characteristic discontinuous Galerkin (CDG) advection scheme was presented for tracer transport. The scheme is conservative, unconditionally stable with res…