We have introduced a fully second order IMplicit/EXplicit (IMEX) time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22, 24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations...

In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACx) [4], a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) [5] as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and EN0 schemes for solving the Euler and MHD equations ...

The use of computational techniques that solve the Euler or the Navier-Stokes equations are increasingly being used by competing syndicates in races like the Americas Cup. For sail configurations, this desire stems from a need to understand the influence of the mast on the boundary layer and pressure distribution on the main sail, the effect of camber and planform variations of the sails on the...

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) t...

This paper presents a well-balanced two-dimensional (2D) finite volume model to simulate the propagation, runup and rundown of long wave. Non-staggered grid is adopted to discretize the governing equation and the intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for wate...

This paper describes a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear PDE, whose solutions are called hydrostatic equilibria. We present a well-balanced method, meaning that besides discretizi...

HPRC (High-Performance Reconfigurable Computing) systems include multicore processors and reconfigurable devices acting as custom coprocessors. Due to economic constraints, the number of reconfigurable devices is usually smaller than the number of processor cores, thus preventing that a 1:1 mapping between cores and coprocessors could be achieved. This paper presents a solution to this problem,...

A new ®nite element model has been developed to simulate two-dimensional free surface ̄ow in rivers and estuaries. The variables of the model are the speci®c discharge and the water level. The algorithm takes into account the natural boundaries of the ̄ow, de®ned by the contour lines of zero depth, with a new approach that accepts positive and negative values for the water depth. In this way, we...

Directional wave energy focusing in space is one of the mechanisms that may contribute to the generation of a rogue wave in the ocean. To this effect, in this paper, we study the generation of extreme waves in a three-dimensional numerical wave tank from the motion of a snake wavemaker. The numerical model solves incompressible fully nonlinear free-surface Euler equations for potential flow, us...

We describe our investigation of a fast 3D finite element method (FEM) for biomedical simulation of a muscle-activated human tongue. Our method uses a linear stiffness-warping scheme to achieve simulation speeds which are within a factor 10 of real-time rates at the expense of a small loss in accuracy. Muscle activations are produced by an arrangement of forces acting along selected edges of th...