On the Convergence of the Convectively Filtered Burgers Equation to the Entropy Solution of the Inviscid Burgers Equation

2008/05/14 by Greg Norgard, Norgard, Greg, Kamran Mohseni +1 · 1 citation
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.0805.2176

openalex publication_date 2008/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then the results are extended to encompass more general initial conditions.

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