Adaptive Mesh Refinement for One Dimensional Scalar Conservation Laws

Date

2024-9-6

Author

Çar, Kadir

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This thesis examines the numerical solutions of one dimensional scalar conservation laws on non-uniform grids by considering an Adaptive Mesh Refinement (AMR) based on an algorithm proposed by Berger and Colella. Finite volume method is used for discretization of the test equations with the CLAWPACK software. Three basic equations in one dimension are of particular interest; linear advection equation, inviscid Burgers equation, and Buckley-Leverett equation. Propagation of shock and rarefaction waves are investigated and compared for both standard uniform mesh and AMR at different time levels with smooth and piecewise smooth initially given functions. The findings demonstrate that results by AMR offer superior efficiency by focusing computational resources where needed, reducing overall costs while preserving accuracy. This comparison underscores the advantages of adaptive strategies in managing sharp gradients and complex wave propagation in one dimensional scalar conservation laws.

Subject Keywords

Scalar conservation law, linear advection equation, inviscid Burgers equation, Buckley-Leverett equation, Adaptive Mesh Refinement

URI

https://hdl.handle.net/11511/111037

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Graduate School of Natural and Applied Sciences, Thesis