A finite point method for compressible flow

Abstract

SUMMARYA weighted least squares ÿnite point method for compressible ow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based ÿnite volume or ÿnite element techniques, making the present ÿnite point method competitive.

Simulation of the acoustic wave propagation using a meshless method

“…[7,10,11]. The interpolation condition in the WLSQ approach allows to simplify the left side of the equation system (15) avoiding the necessity to solve the system of n linear equations.…”

“…Therefore, using WLSQ with interpolation condition greatly reduces the computation costs and improves stability, cf. [10,11]. The system of ODE (15) is then solved with high order lowdissipation and low-dispersion runge-kutta scheme optimized for wave propagation problems, cf.…”

“…[3,4], have been investigated in this context, but there is also growing interest in meshless methods, cf. [5][6][7][8][9][10][11], due to their potential advantages. Depending on applications, these methods can be superior in accuracy, stability, robustness and can deal with complex geometries, multiphase flow, problems with free boundaries and moving objects.…”

A finite point method for adaptive three‐dimensional compressible flow calculations

“…Since the FPM appeared in the literature towards the mid-nineties, it has been successfully applied to solve convective-diffusive problems, incompressible and compressible fluid flow problems [9,10,11,12,13,14] and solid mechanics problems [15,16,17] among others. As regards to fluid flow problems, the first application of the FPM to the solution of the twodimensional compressible flow equations was presented by Oñate et al [8,9] and Fischer [12].…”

“…In relation to the solution of the incompressible flow equations, a fractional step algorithm stabilized via a technique known as Finite Calculus (FIC) [18] has also been successfully employed. The FP solution of the three-dimensional compressible flow equations was presented in a pioneer work by Löhner et al [14]. There, two contributions are well worth mentioning: a reliable procedure for constructing the local clouds (based on a Delaunay technique) and a well-suited upwind biased scheme for solving the flow equations.…”