Examinando por Materia "Wave equations"

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    Analysis of the stability and dispersion for a Riemannian acoustic wave equation
    (ELSEVIER SCIENCE INC, 2019-01-15) Quiceno, H. R.; Arias, C.; Quiceno, H. R.; Arias, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The construction of images of the Earth's interior using methods as reverse time migration (RTM) or full wave inversion (FWI) strongly depends on the numerical solution of the wave equation. A mathematical expression of the numerical stability and dispersion for a particular wave equation used must be known in order to avoid unbounded numbers of amplitudes. In case of the acoustic wave equation, the Courant–Friedrich–Lewy (CFL) condition is a necessary but is not a sufficient condition for convergence. Thus, we need to search other types of expression for stability condition. In seismic wave problems, the generalized Riemannian wave equation is used to model their propagation in domains with curved meshes which is suitable for zones with rugged topography. However, only a heuristic version of stability condition was reported in the literature for this equation. We derived an expression for stability condition and numerical dispersion analysis for the Riemannian acoustic wave equation in a two-dimensional medium and analyzed its implications in terms of computational cost. © 2018 Elsevier Inc.
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    Solución aproximada de la ecuación KdV por el método de los elementos finitos Taylor - Petrov - Galerkin
    (Universidad EAFIT, 2014) Buitrago García, Lida; Villegas Gutiérrez, Jairo Alberto
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    Solution of the Navier - Stokes equation using the method of characteristic curves
    (Universidad EAFIT, 2014) Villegas Jiménez, José David; García Ruíz, Manuel Julio
    This project deals about the solution of the Navier Stokes Equations by the Method of Characteristics -- This method is used to eliminate the convective part of equations of the convection-diffusion type, conducting the material derivative in a Lagrangian manner along the characteristic curves of each node in a fixed grid -- Following this approach, the method is able to solve the incompressible Navier Stokes Equations with the advantage of using large timesteps -- In the present case, the solution of the well known Lid Driven Cavity Flow problem is obtained for several Reynolds numbers, showing good agreement when compared to solutions obtained by other methods
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    The Spectral Cell Method in Nonlinear Earthquake Modeling
    (Universidad EAFIT, 2016) Giraldo Cuartas, Daniel; Restrepo Sánchez, Doriam Leidin
    In this study we focus at examining an efficient high order finite element strategy to compute the dynamic response of heterogeneous basins under nonlinear soil behavior subjected to point-source earthquake events -- The numerical technique known as the Spectral Cell Method (SCM) combines Fictitious-Domains concepts with the Spectral-version of the finite element method to accurately solve the wave equations in heterogeneous geophysical domains -- We tested the SCM in physically and computationally challenging domains namely, (i) a semi-elliptical basin, and (ii) an undulated basin embedded in a half-space with several irregular geological structures with different material discontinuities -- Nonlinear behavior is considered by implementing a Mohr-Coulomb, and a Drucker- Prager yielding criteria -- We benchmark our simulations with results obtained using MIDAS GTS NX, a finite element tool for geotechnical applications based upon traditional boundary-fitted meshing techniques