A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...

In the present study, stress analysis and explicit solution of rectangular plate with arbitrarily located circular hole, subjected to linear normal stresses on two opposite edges, has been investigated. Airy function and hoop stresses occurring at the edge of the circular have been computed. In this method 2D dimension elasticity and Airy stress function was used. The present method for explici...

We study here explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data in L(R). Under a stability condition on the time step, we prove the convergence of the finite volume approximation towards the unique stochastic entropy solution of the equation.

The main purpose of the present work is multi-objective shape optimization of a projectile tip for impacting and normal penetrating. Velocity drop, weight and inner volume of projectile have been considered as three conflicting objective functions.  For this purpose, at the first step, finite element modeling was done using ABAQUS/Explicit and projectile penetration was examined in different ge...

1. Lax equivalence theorem 1 2. Abstract error analysis 2 3. Application: Finite difference method 3 4. Application: Finite element method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming finite element methods 7 8. Application: Finite volume method 7 9. Application: Superconvergence of linear finite e...

We construct a parallel algorithm, suitable for distributed memory architectures, of an explicit shock-capturing finite volume method for solving the two-dimensional shallow water equations. The finite volume method is based on the very popular approximate Riemann solver of Roe and is extended to second order spatial accuracy by an appropriate TVD technique. The parallel code is applied to dist...