We address the numerical simulation of fluid-structure interaction problems dealing with an incompressible fluid whose density is close to the structure density. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and...

Abstract. In this paper, we present a local discontinuous Galerkin (LDG) method and two unconditionally energy stable schemes for the phase field crystal (PFC) equation. The semidiscrete energy stability of the LDG method is proved first. The PFC equation is a sixth order nonlinear partial differential equation (PDE), which leads to the severe time step restriction (Δt = O(Δx6)) of explicit tim...

A numerical method for the two-dimensional, incompressible Navier–Stokes equations in vorticity-streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the reconstruction of the streamfunction. A descrip...

The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyse the properties of the Rothe method concerning stability and convergence for this kind of systems. For this, we c...

In a previous paper [4], we adapted Nitsche’s method for the approximation of the linear elastodynamic unilateral contact problem. The space semi-discrete problem was analyzed and some schemes (θ-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed under appropriate CFL conditons. In the present paper we look at the stability properties of the above-mentioned schem...

In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular...

Abstract. An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-...

Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in the water is integrated in time using a semi-implicit time discretization of the adiabatic Euler equations. Results are presented either using a non-conservative semi-implicit...

The nite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular nite elements are attractive for ocean modeling because of their exibility for representing irregular boundaries and for local mesh re nement. A \kriging" interpolator is used for the semi-Lagrangian advection, leading to an acc...

An efficient adaptive moving mesh method for investigation of the semi-classical limit of the focusing nonlinear Schrödinger equation is presented. The method employs a dynamic mesh to resolve the sea of solitons observed for small dispersion parameters. A second order semi-implicit discretization is used in conjunction with a dynamic mesh generator to achieve a cost-efficient, accurate, and st...