Semi-implicit, semi-Lagrangian modelling for environmental problems on staggered Cartesian grids with cut cells

Rosatti, Giorgio; Cesari, D.; Bonaventura, Luca

doi:10.1016/j.jcp.2004.10.013

Cited by 40 publications

(43 citation statements)

References 35 publications

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“…There has been a renewed interest in the development of Cartesian-grid-based techniques for dealing with problems defined in geometrically-complicated domains (e.g. [14][15][16][17][18][19]). …”

Section: Introductionmentioning

confidence: 99%

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Mai‐Duy

Le-Cao

Tran-Cong

2007

Numerical Methods in Fluids

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This paper reports a radial-basis-function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of high-order derivatives. The method is applied to simulate thermally-driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleighnumber solutions are achieved and they are in good agreement with previously published numerical data.

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Section: Introductionmentioning

confidence: 99%

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Mai‐Duy

Le-Cao

Tran-Cong

2007

Numerical Methods in Fluids

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“…By contrast, our primary motivation for using polyhedral interpolation is that it enables the interpolated velocity to closely conform to the geometry of solid boundaries. Rosatti et al (ROSATTI;CESARI;BONAVENTURA, 2005) presented a related two-dimensional technique that fits boundary-respecting linear velocity fields to the triangular, trapezoidal, and pentagonal cells resulting from the usual marching-squares cases applied to an implicit representation of the solid boundary. Our approach clips the regular grid against the solid boundary triangle mesh, yielding arbitrary polyhedral cells.…”

Section: Interpolationmentioning

confidence: 99%

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

2016

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Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

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“…The scaling parameter in the radial kernel was chosen in general according to the suggestion in [19], e.g. by assigning to it a value of the same order of magnitude as the size of the computational domain.…”

Section: Comparisons Between Gaussian Kernels and Rt Elementsmentioning

confidence: 99%

Kernel‐based vector field reconstruction in computational fluid dynamic models

Bonaventura

Iske

Miglio

2011

Numerical Methods in Fluids

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SUMMARYKernel-based reconstruction methods are applied to obtain highly accurate approximations of local vector fields from normal components assigned at the edges of a computational mesh. The theoretical background of kernel-based reconstructions for vector-valued functions is first reviewed, before the reconstruction method is adapted to the specific requirements of relevant applications in computational fluid dynamics. To this end, important computational aspects concerning the design of the reconstruction scheme like the selection of suitable stencils are explained in detail. Extensive numerical examples and comparisons concerning hydrodynamic models show that the proposed kernel-based reconstruction improves the accuracy of standard finite element discretizations, including Raviart-Thomas (RT) elements, quite significantly, while retaining discrete conservation properties of important physical quantities, such as mass, vorticity, or potential enstrophy.

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Semi-implicit, semi-Lagrangian modelling for environmental problems on staggered Cartesian grids with cut cells

Cited by 40 publications

References 35 publications

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

Kernel‐based vector field reconstruction in computational fluid dynamic models

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