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    Fast, Robust, Iterative Riemann Solvers for the Shallow Water and Euler Equations

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    Thesis_Carlos_Munoz_Final.pdf
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    Description:
    MS Thesis
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    Type
    Thesis
    Authors
    Muñoz-Moncayo, Carlos cc
    Advisors
    Ketcheson, David I. cc
    Committee members
    Tzavaras, Athanasios cc
    Truscott, T. T. cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2022-07-12
    Permanent link to this record
    http://hdl.handle.net/10754/679750
    
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    Abstract
    Riemann problems are of prime importance in computational fluid dynamics simulations using finite elements or finite volumes discretizations. In some applications, billions of Riemann problems might need to be solved in a single simulation, therefore it is important to have reliable and computationally efficient algorithms to do so. Given the nonlinearity of the flux function in most systems considered in practice, to obtain an exact solution for the Riemann problem explicitly is often not possible, and iterative solvers are required. However, because of issues found with existing iterative solvers like lack of convergence and high computational cost, their use is avoided and approximate solvers are preferred. In this thesis work, motivated by the advances in computer hardware and algorithms in the last years, we revisit the possibility of using iterative solvers to compute the exact solution for Riemann problems. In particular, we focus on the development, implementation, and performance comparison of iterative Riemann solvers for the shallow water and Euler equations. In a one-dimensional homogeneous framework for these systems, we consider several initial guesses and iterative methods for the computation of the Riemann solution. We find that efficient and reliable iterative solvers can be obtained by using recent estimates on the Riemann solution to modify and combine well-known methods. Finally, we consider the application of these solvers in finite volume simulations using the wave propagation algorithms implemented in Clawpack.
    Citation
    Muñoz-Moncayo, C. (2022). Fast, Robust, Iterative Riemann Solvers for the Shallow Water and Euler Equations [KAUST Research Repository]. https://doi.org/10.25781/KAUST-W91M5
    DOI
    10.25781/KAUST-W91M5
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-W91M5
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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