Abstract

One of the greatest challenges in our days continues being to design numerical methods capable of approaching the solution of partial differential equations in a fast and precise way. One of the most important equations, due to the hydraulic and transport applications that it has, and the great amount of difficulties that it usually presents when resolving it numerically is the Advection Equation. In the present work we present a Method of Lines applied to the numerical solution of said equation in irregular regions making use of a Generalized Finite Differences scheme. A series of numerical tests and results are presented, which show the accuracy of the proposed method.