Lattice Boltzmann schemes rely on the enlargement of size target problem in order to solve PDEs a highly parallelizable and efficient kinetic-like fashion, split into collision stream phase. This structure, despite well-known advantages from computational standpoint, is not suitable construct rigorous notion consistency with respect equations provide precise stability. In alleviate these shorta...

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...

We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order k 0 at mesh faces. The method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions. Fairly general meshes with polytopal and nonmatching cells are suppor...

We present a new high-order, local meshfree method for numerically solving reaction diffusion equations on smooth surfaces of codimension 1 embedded in Rd. The novelty of the method is in the approximation of the Laplace–Beltrami operator for a given surface using Hermite radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact (or implicit) RBF gener...

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...