4 papers
New Adaptive Numerical Methods Based on Dual Formulation of Hyperbolic Conservation Laws
Alina Chertock, Qingcheng Fu, Alexander Kurganov +1
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solu…
New Smoothness Indicator Within an Active Flux Framework
Alina Chertock, Alexander Kurganov, Lorenzo Micalizzi
In this work, we introduce a new smoothness indicator (SI), which is capable of detecting ``rough'' parts of the solutions computed by active flux (AF) methods for hyperbolic (syst…
Dual Formulation Finite-Volume Methods on Overlapping Meshes for Hyperbolic Conservation Laws
Rémi Abgrall, Alina Chertock, Alexander Kurganov +1
In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgral…
Algorithms of very high space-time orders of accuracy for hyperbolic equations in the semidiscrete WENO-DeC framework
Lorenzo Micalizzi, Eleuterio F. Toro
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis o…