Simulation of compressible flows became a routine activity with the appearance of shock-
/contact-capturing methods. These methods can determine all waves, particularly …

In recent years numerical methods have been widely used to effectively resolve complex
flow features of aerodynamics flows with meshes that are reasonable for today's computers …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new
but have gained rapid popularity in numerical solutions of hyperbolic partial differential …

In this article, a conservative least-squares polynomial reconstruction operator is applied to
the discontinuous Galerkin method. In a first instance, piecewise polynomials of degree N …

This book is an introductory text to a range of numerical methods used today to simulate time-
dependent processes in Earth science, physics, engineering, and many other fields. The …

We present a new numerical method to solve the heterogeneous elastic wave equations
formulated as a linear hyperbolic system using first-order derivatives with arbitrary high …

We present a new numerical approach to solve the elastic wave equation in heterogeneous
media in the presence of externally given source terms with arbitrary high-order accuracy in …

In this article we present a non-oscillatory finite volume scheme of arbitrary accuracy in
space and time for solving linear hyperbolic systems on unstructured grids in two and three …