As the total value of the global financial market outgrew the value of the real economy,
financial institutions created a global web of interactions that embodies systemic risks …

Nonlinear convective terms pose the most critical issues when a numerical discretization of
the Navier–Stokes equations is performed, especially at high Reynolds numbers. They are …

Many processes in science and engineering can be described by partial differential
equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics …

We present and analyze an entropy-stable semi-discretization of the Euler equations based
on high-order summation-by-parts (SBP) operators. In particular, we consider general …

The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is
a framework of high order methods for conservation laws, unifying some discontinuous …

New Pell polynomials in two dimensions together with many important properties are
presented in this work. The two dimensions Pell polynomials expansion coefficients of a first …

An accurate and efficient time-dependent wave packet method is proposed for solving the
product state-resolved reaction probabilities of the tetratomic reactive system. In this method …

In this work we study the performance of some variational multiscale models (VMS) in the
large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by …

This paper presents two kinds of strategies to construct structure-preserving algorithms with
homogeneous Neumann boundary conditions for the sine-Gordon equation, while most …

The construction of high order entropy stable collocation schemes on quadrilateral and
hexahedral elements has relied on the use of Gauss--Legendre--Lobatto collocation points …