Moving mesh solutions of the relativistic Burgers-FLRW models
B. Okutmuştur (Middle East Technical University)
Cornelis Vuik (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Kadir Yigit (Middle East Technical University)
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Abstract
This work presents a novel investigation of the recently derived relativistic Burgers-FLRW model, a scalar hyperbolic balance law with nontrivial source terms, using the Moving Mesh Method (MMM). Building on an MMM framework originally developed for hyperbolic conservation laws, we examine a range of monitor and smoothing functions to identify effective combinations for accurately resolving key solution features while reducing computational error. Numerical experiments compare the MMM with Adaptive Mesh Refinement (AMR) and uniform mesh discretizations. An L1-error analysis is used to study the effect of different monitor functions, explore the role of various β parameters, and directly compare the performance of the MMM and AMR strategies. The results show that both adaptive approaches provide higher accuracy and better efficiency than uniform meshes, while also offering a clear comparison between MMM and AMR and practical insight into mesh adaptation for scalar balance laws.
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