A family of moment-conserving advection schemes in 1-D was introduced by van Leer in the mid 1970s. Of these, MUSCL advection is the best known. That advection scheme represents the advected function, which we will call a , by a linear function within each grid cell. The linear function is determined by the values of the first two moments of this density distribution within the cell, namely the...

This paper presents a class of new second-order accurate (IK + 3)-point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a CFL restriction of K. These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate (IK + l)-point scheme to a modified flux. The so-derived second-order accura...

In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant number less than 1. In this paper, we will show that for scalar conservation laws, for any fixed C...

This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via explicit calculations. The selection strategy consists of the following steps. First, using the explicit scheme, we calculate the solution at a new time level. ...

because it is not possible to recognize the mechanism of cantilever failure in field studies, this type of common failure in riverbanks is investigated in the laboratory. for this purpose, two samples of susceptible soil that forms an overhanging block in riverbanks are used for physical model tests to determine their physical, chemical and mechanical characteristics. soil blocks of different d...

We consider the chemical vapor deposition process on a trenched Si-substrate. To understand the process (e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to huge difference in the sizes of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a mu...

We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resul...

We establish a ternary Cahn-Hilliard type Nakazawa-Ohta phase-field model for the triblock copolymer, and study its numerical approximation. The is highly coupled nonlinear system, consisting of two equations nonlocal equations. solve by constructing second-order accurate, time-marching scheme via Scalar Auxiliary Variable (SAV) approach combined with stabilization technique. At every time step...