Doctorado en Ingeniería Matemática (tesis)

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A Class of Conservative Lagrangian-Eulerian Methods on Triangular Grids for Hyperbolic Problems : Design, Analysis and Applications
(Universidad EAFIT, 2024) Agudelo Quiceno, Jorge Eliécer; Pérez Sepúlveda, John Alexander; Cano Sánchez, José Albeiro
In this thesis, we construct, analyze and implement a class of fully-discrete and semi-discrete schemes on triangular grids intended to numerically solve initial value problems involving multidimensional hyperbolic conservation and balance laws, both scalar and systems. The construction of this novel class of schemes is based on the no-flow surface/curve concept and introduces an effective class of numerical fluxes that do not require constructing or evaluating the Jacobian matrix of the respective flux functions. The implementation of the new fully-discrete and semi-discrete Lagrangian-Eulerian schemes, , in the solution of nontrivial scalar and systems problems, is performed using a weak CFL-type stability condition that is independent of the eigenvalues (exact and approximate values) of the relevant Jacobian of the numerical flux functions, and without the need for high-resolution reconstruction procedures.