Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. Th...

Given an ordinary differential equation on a homogeneous manifold, one can construct a “geometric integrator” by determining a compatible ordinary differential equation on the associated Lie group, using a Lie group integration scheme to construct a discrete time approximation of the solution curves in the group, and then mapping the discrete trajectories onto the homogeneous manifold using the...

Higher-order compact difference schemes can achieve higher order accuracy on uniform grids. However, in some cases these may not achieve the desired accuracy. Therefore, this paper proposes a multigrid method based on higher-order compact difference scheme for 3D Helmholtz equation on nonuniform grids. Interpolation and restriction operators are designed accordingly. The suggested scheme has up...

Abstract. We are concerned with the detection of edges – the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our...

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on gener...

Ethical tenets and political systems are one of the most controversial terminologiesin philosophy ofethics and politicalthought.That is why thinkers based upon theirintellectual  standpoint  have  reached  different  inferences  and  definitions  andelaborated  various  aspects  of  it  accordingly.Shariatisimilar  to  his  precedingthinkersmade the creation of ethicalpolitical system one of hi...