Equal-area method for scalar conservation laws
Marjeta Kramar Fijav\v{z}, Mitja Lakner, Marjeta \v{S}kapin Rugelj
TL;DR
This paper introduces a straightforward numerical method based on the equal-area principle for efficiently computing the unique entropy solution to one-dimensional scalar conservation laws.
Contribution
It presents a novel equal-area based approach that directly computes solutions at given times, simplifying the numerical process for scalar conservation laws.
Findings
Method effectively computes entropy solutions
Simplifies numerical solution process
Provides direct solution at specified times
Abstract
We study one-dimensional conservation law. We develop a simple numerical method for computing the unique entropy admissible weak solution to the initial problem. The method basis on the equal-area principle and gives the solution for given time directly.
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Taxonomy
TopicsFluid Dynamics and Turbulent Flows · Computational Fluid Dynamics and Aerodynamics · Wind and Air Flow Studies