Bibliographic citations
Chávez, X., (2018). Resolución de la ecuación de advección lineal unidimensional por un método de volúmenes finitos compacto de alto orden [Tesis, Pontificia Universidad Católica del Perú]. http://hdl.handle.net/20.500.12404/10048
Chávez, X., Resolución de la ecuación de advección lineal unidimensional por un método de volúmenes finitos compacto de alto orden [Tesis]. PE: Pontificia Universidad Católica del Perú; 2018. http://hdl.handle.net/20.500.12404/10048
@mastersthesis{renati/17540,
title = "Resolución de la ecuación de advección lineal unidimensional por un método de volúmenes finitos compacto de alto orden",
author = "Chávez Pacheco, Xyoby",
publisher = "Pontificia Universidad Católica del Perú",
year = "2018"
}
The numerical methods of high order, necessary for spatial discretization, are one of the most active areas of the field of Computational Fluid Dynamics. Within these, Finite Volume Methods (abbreviated as MVF in spanish) have encountered difficulties in the implementation of reconstruction processes. In the present work we present a novel high order compact reconstruction process proposed by Q. Wang [22], and implemented in Python. The novelty lies in that high order is achieved using a compact stencil, that is, using only neighboring cells. In this process we obtain a set of relations that are constructed to obtain the coefficients of reconstruction polynomials on the control volumes of interest, preserving their average values and that of their derivatives. With these relations we obtain an overdetermined linear system that is adjusted by least squares resulting in a tridiagonal system by blocks in the case of a 1D advection equation. For this advection equation we also use the Fourier Analysis to examine the wave numbers modified by the compact MVF. The reconstruction includes parameters that are optimized to improve the dispersion / dissipation properties. Furthermore, the von Neumann stability analysis allows us to estimate the maximum CFL number for two Runge-Kutta methods. Finally, we validate the convergence orders of the combination of the compact MVF with two schemes of Runge-Kutta and we also validate the optimal parameters of the reconstruction schemes.
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