In this paper we present a high-order accurate cell-centered finite volume method for the semi-implicit discretization of multidimensional hyperbolic systems in conservative form on unstructured grids. This method is based on a special splitting of the physical flux function into a convective and a non-convective part. The convective contribution to the global flux is treated implicitly by mimi...

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier–slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite element method, where the velocity and vorticity is approximated with the divand curlconforming Né...

A fully discrete finite element method, based on a new weak formulation and time-stepping scheme, is proposed for the surface diffusion flow of closed curves in two-dimensional plane. It proved that method can preserve two geometric structures simultaneously level, i.e., perimeter curve decreases time while area enclosed by conserved. Numerical examples are provided to demonstrate convergence e...

In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties deal the richness scales many flows. These must also easy implement within current complex, possibly legacy codes. Herein we develop, analyze and test new stepping addressing these two issues goal accelerating development needs applications. The are crea...

Solving an evolution problem in parallel is naturally undertaken by trying to paral13 lelize the algorithm in space, and then still follow a time stepping method from the 14 initial time t = 0 to the final time t = T . This is especially easy to do when an explicit 15 time stepping method is used, because in that case the time step for each component 16 is only based on past, known data, and th...

The Discontinuous Galerkin Time Domain (DGTD) methods are now widely used for the solution of wave propagation problems. Able to deal with unstructured meshes past complex geometries, they remain fully explicit with easy parallelization and extension to high orders of accuracy. Still, modal or nodal local basis functions have to be chosen carefully to obtain actual numerical accuracy. Concernin...

Despite recent findings [1] on the superiority of monolithic approaches to FSI over the segregated ones, there are many advantages that make the latter a valuable alternative [2]. For example, in a staggered approach, individual solution strategies can be employed independently to fluid flow and solid dynamics and they can be coupled through a robust interface coupling methods. This allows rese...

This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

The Gray–Scott (GS) model is a non-linear system of equations generally adopted to describe reaction–diffusion dynamics. In this paper, we discuss numerical scheme for solving the GS system. diffusion coefficients are on surfaces and they depend space time. regard, first adopt an implicit difference stepping method semi-discretize in time direction. Then, implement hybrid advanced meshless disc...