Balance laws arise from many areas of engineering practice specifically from the fluid mechanics. Many numerical methods for the solution of these balanced laws were developed in recent decades. The numerical methods are based on two views: solving hyperbolic PDE with a nonzero source term (the obvious description of the central and central-upwind schemes; (Kurganov & Levy, 2002; LeVeque, 2004)...

In his classic book, Modern Algebra, van der Waerden gave a procedure for factoring polynomials over a …nite-dimensional, separable, simple extension …eld. I believe that there is a nonconstructive component to his proof, and I will indicate where it comes in and why. Although I’m sure that this component could be avoided while staying within the framework that he set down, it is simpler to get...

A validation study is presented for a numerical code which calculates a two-dimensional steady-state solution for inviscid hypersonic flows in the presence of strong surface blowing. A higher-orde: Godunov-type finite-volume approach is used to discretize the inviscid Euler equations. Interface values of the state quantities are reconstructed nsing a monotone interpolation technique suggested b...

Van Allen radiation belts consist of relativistic electrons trapped by Earth's magnetic field. Trapped electrons often drift azimuthally around Earth and display a butterfly pitch angle distribution of a minimum at 90° further out than geostationary orbit. This is usually attributed to drift shell splitting resulting from day-night asymmetry in Earth's magnetic field. However, direct observatio...

When utilizing a finite volume method to predict outburst flood evolution in real geometry, the processing of wet-dry front and dry cells is an important step. In this paper, we propose new approach process cells, including four steps: (1) estimating intercell properties; (2) modifying interface elevation; (3) calculating cell elevations by averaging elevations; (4) changing value first term sl...

To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are associated with the transition to a new formulation of the problem, where the fluxes (derivatives with respect to a spatial direction) are treated as unknown quantit...

In the context of low Mach number flows, successful methods are Asymptotic Preserving and IMEX schemes. Both schemes for hyperbolic equations rely on a splitting of the convective flux into stiff and nonstiff parts. This choice is not arbitrary and has an influence on both the stability and the accuracy of the resulting methods. In this work, we consider a first-order IMEX scheme based on diffe...