Commutative discrete filtering on unstructured grids based on least-squares techniques
نویسندگان
چکیده
The present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions. First, building on the work of Marsden et al. [J. Comp. Phys. 175 (2002) 584], a new commutative discrete filter based on least-squares techniques is constructed. Second, a new analysis of the discrete commutation error is carried out. The analysis indicates that the discrete commutation error is not only dependent on the number of vanishing moments of the filter weights, but also on the order of accuracy of the discrete gradient operator. The results of the analysis are confirmed by grid-refinement studies. 2003 Elsevier Science B.V. All rights reserved.
منابع مشابه
High-order finite volume schemes on unstructured grids using moving least-squares reconstruction. Application to shallow water dynamics
This paper introduces the use of moving least-squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh-free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the s...
متن کاملMultigrid Methods for the Stokes Equations using Distributive Gauss-Seidel Relaxations based on the Least Squares Commutator
A distributive Gauss–Seidel relaxation based on the least squares commutator is devised for the saddle-point systems arising from the discretized Stokes equations. Based on that, an efficient multigrid method is developed for finite element discretizations of the Stokes equations on both structured grids and unstructured grids. On rectangular grids, an auxiliary spacemultigridmethod using onemu...
متن کاملA meshless discrete Galerkin method for solving the universe evolution differential equations based on the moving least squares approximation
In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...
متن کاملResolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme
CFD has become more and more used in the industry for the simulation of flows. Nevertheless, the complex configurations of real engineering problems make difficult the application of very accurate methods that only works on structured grids. From this point of view, the development of higher order methods for unstructured grids is desirable. The finite volume method can be used with unstructure...
متن کاملDiscrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data
Spherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analys...
متن کامل