Abstract. In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow ũ0, ṽ0, and φ̃0 (subor super-critical flow at each part of the boundary). The three cases that we consid...

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We consider a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3 + 1 formulation an...

The stability behavior of low immersion helical end milling processes is investigated in this paper. Low radial immersion milling operations involve interrupted cutting which induces chatter vibration under certain cutting conditions. Time Finite Element Analysis (TFEA) is suggested for an approximate solution for delayed differential equations encountered during interrupted milling. An improve...