27 citations · 49 across the 6 of their papers we have counts for
11 papers
A Hybrid Adaptive Low-Mach-Number/Compressible Method: Euler Equations
Emmanuel Motheau, Max Duarte, Ann Almgren +1
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computation…
High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs
Max Duarte, Richard Dobbins, Mitchell Smooke
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems dis…
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
Stéphane Descombes, Max Duarte, Thierry Dumont +3
A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator…
A Low Mach Number Model for Moist Atmospheric Flows
Max Duarte, Ann Almgren, John Bell
We introduce a low Mach number model for moist atmospheric flows that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rath…
High order schemes based on operator splitting and deferred corrections for stiff time dependent PDEs
Max Duarte, Matthew Emmett
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonl…
Analysis of operator splitting in the non-asymptotic regime for nonlinear reaction-diffusion equations. Application to the dynamics of premixed flames
Stéphane Descombes, Max Duarte, Thierry Dumont +3
In this paper we mathematically characterize through a Lie formalism the local errors induced by operator splitting when solving nonlinear reaction-diffusion equations, especially…