We present a general technique to solve Partial Differential Equations, called robust stencils, which make them tolerant to soft faults, i.e. bit flips arising in memory or CPU calculations. We show how it can be applied to a two-dimensional Lax-Wendroff solver. The resulting 2D robust stencils are derived using an orthogonal application of their 1D counterparts. Combinations of 3 to 5 base ste...

In this paper, we implement energy equation coupled with viscous Burgers’ as a mathematical model for the estimation of thermal pollution river water. The is nonlinear system partial differential equations (PDEs) that read an initial and boundary value problem (IBVP). For numerical solution IBVP, investigate explicit second-order Lax- Wendroff type scheme parabolic PDEs. We present solutions gr...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

The goal of this work is to introduce new families shock-capturing high-order numerical methods for systems conservation laws that combine Fast WENO (FWENO) and Optimal (OWENO) reconstructions with Approximate Taylor the time discretization. FWENO are based on smoothness indicators require a lower number calculations than standard ones. OWENO definition nonlinear weights allows one unconditiona...

This paper introduces the use of moving least-squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh-free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the s...