This paper presents an efficient Euler method on Cartesian grids coupled with an integral Boundary-Layer method. The unsteady Euler equations are solved using cell-centered finite volume method by the implicit-explicit dual-time stepping scheme. The wall boundary conditions on the wing are implemented on the wing chord plane by first order approximation so that non-moving Cartesian grids can be...

We present our computational method for binary alloy solidification which takes advantage of high performance computing where up to 1024 cores are employed. Much of the simulation at a sufficiently fine resolution is possible on a modern 12 core PC and the 1024 core simulation is only necessary for very mature dendrite and convergence testing where high resolution puts extreme demands on memory...

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible Navier-Stokes equations with bending forces. Here, we closed enforce conservation of the enclosed volume. The numerical approach builds on higher order parameterizations, Taylor-Hood element for part, appropriate approximations geometric...

We present an efficient, implicit-explicit numerical method for wave propagation in solids containing fluid-filled cracks, motivated by applications in geophysical imaging of fractured oil/gas reservoirs and aquifers, volcanology, and mechanical engineering. We couple the elastic wave equation in the solid to an approximation of the linearized, compressible Navier–Stokes equations in curved and...

We describe our experiences running PFLOTRAN—a code for simulation of coupled hydro-thermal-chemical processes in variably saturated, non-isothermal, porous media—on the Cray XT series of computers, including initial experiences running on the petaflop incarnation of Jaguar, the Cray XT5 at the National Center for Computational Sciences at Oak Ridge National Laboratory. PFLOTRAN utilizes fully ...

We present an asymptotic preserving (AP), large time-step scheme for the shallow water equations in the low Froude number limit. Based on a multiscale asymptotic expansion, the momentum fluxes are split into a nonstiff and a stiff part. A semi-implicit discretisation, where the nonstiff terms are treated explicitly and stiff terms implicitly in time, is crucial to achieve the AP property. A com...

We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jumpdiffusion process. We discuss localization to a finite domain and provide an estimate for the localization ...

We make an initial investigation into the numerical efficiency of a fully discrete summation-by-parts approach for unsteady flows. As a model problem for the Navier-Stokes equations we consider a two-dimensional advectiondiffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summation-by-parts form together with weak boundary condi...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...