The solution algorithm used in CarbTool is based on the finite difference method (FDM), and the code is developed using Microsoft Visual C++ in Window OS. The tool has been built on the concept of the carbon flux at the surface between the gas and steel is to be specified by the user. The outputs of CarbTool are the carbon concentration distribution profile inside the steel part and the surfa...

The finite volume method combines the advantage of the finite element method and the finite difference method, while overcoming their shortcomings. This paper describes the development of the finite volume method and the process of using finite volume method for fluid calculations. Finally, this paper introduces the process of using improved finite volume method for solving the flow equations o...

A new method combining a finite difference method and a reduced order model (ROM) algorithm is presented for twodimensional (2-D) electromagnetic problems. The problem space is subdivided into subdomains of a generic type. By discretizing the spatial derivatives in a way similar to the finite-difference in time-domain technique (FDTD), the state equations are written down in each subdomain. Fro...

The cervix is a biochemically active tissue that changes its biomechanical properties in a remodeling process during pregnancy to be prepared for parturition. This maturation process is associated with changes of the mechanical properties of the cervical stroma. Preterm delivery is connected with undesired cervical changes bound to cervical ripening. Non-destructive evaluation using ultrasonic ...

Comparisons are made between the finite difference method (FDM) and the control volume formulation (CVF). An analysis of truncation errors for the two methods is presented. Some rules-of-thumb related to the accuracy of the methods are included. It is shown that the truncation error is the same for both methods when the boundary conditions are of the Dirichlet type, the system equations are lin...

The space and time discretization inherent to all FDTD schemes introduce non-physical dispersion errors, i.e. deviations of the speed of sound from the theoretical value predicted by the governing Euler differential equations. A general methodology for computing this dispersion error via straightforward numerical simulations of the FDTD schemes is presented. The method is shown to provide remar...

We study the asymptotics of two space dimensional reaction-diffusion front speeds through mean zero space-time periodic shears using both analytical and numerical methods. The analysis hinges on traveling fronts and their estimates based on qualitative properties such as monotonicity and a priori integral inequalities. The computation uses an explicit second order upwind finite difference metho...

The stability and convergence properties of the mimetic finite difference method for diffusion-type problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved.

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed model ordinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. F...