Finite Difference (FD) methods approximate derivatives of a function by local arguments
(such as du (x)/dx≈(u (x+ h)− u (x− h))/2h, where h is a small grid spacing)–these methods …

Numerical methods for solving the continuum model of the dynamics of the molecular beam
epitaxy (MBE) require very large time simulation, and therefore large time steps become …

Suppressing spurious oscillations is crucial for designing reliable high-order numerical
schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated …

A new simulation approach for high Reynolds number turbulent flows is developed,
combining concepts of monotonicity in nonlinear conservation laws with concepts of large …

In this paper, we investigate the performance of pseudo-spectral methods in computing
nearly singular solutions of fluid dynamics equations. We consider two different ways of …

Low-dimensional flow dynamical systems may converge to erroneous states after long-time
integration, even if they are initialized with the correct state. In this paper, we investigate the …

This is a summary of five lectures delivered at the CIME course on “Advanced Numerical
Approximation of Nonlinear Hyperbolic Equations” held in Cetraro, Italy, on June 1997 …

We develop a method for the modeling of flow discontinuities which can arise as weak
solutions of inviscid conservation laws. Due to its similarity with recently proposed …

This volume contains the texts of the four series of lectures presented by B. Cockburn, C.
Johnson, CW Shu and E. Tadmor at a CIME Summer School. It is aimed at providing a …

We report the development of a discontinuous spectral element flow solver that includes the
implementation of both spectral difference and flux reconstruction formulations. With this …