This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating flow. The method includes dampening scheme that allows large density ratio cases to be simulated. Two verification studies are performed by the relaxation of square droplet surrounded light fluid and bubble rising in denser fluid. is also used simulate collision binary droplets at mod...

In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such s...

This study proposes one-dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank–Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. ...

A procedure to switch the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the develope...

L∞ SOLUTIONS FOR A MODEL OF NONISOTHERMAL POLYTROPIC GAS FLOW∗ HERMANO FRID† , HELGE HOLDEN‡ , AND KENNETH H. KARLSEN‡ Abstract. We establish the global existence of L∞ solutions for a model of polytropic gas flow with varying temperature governed by a Fourier equation in the Lagrangian coordinates. The result is obtained by showing the convergence of a class of finite difference schemes, which...

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for si...