Conservation Properties of Unstructured Staggered Mesh Schemes

By B. Perot. 2000

306 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/28a45338e328179a3b684d1ab687b482ed56b36f

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In Aerospace Engineering

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Direct numerical simulations of turbulent flows over superhydrophobic surfaces (2008, methodology): “There is no numerical viscosity in this scheme (Perot 2000), which is vital to accurately predict the turbulent energy cascade (see Mittal & Moin 1998).”
A numerical method for large-eddy simulation in complex geometries (2004, background): “Exceptions are Perot [31] and Zhang et al. [34] who discuss discrete energy-conservation for staggered schemes on triangular or tetrahedral unstructured grids.”
Structure-preserving discretization of incompressible fluids (2009, background): “The resulting scheme does, however, have most of the numerical properties sought after, including energy conservation over long simulations [22], time reversibility [27], and circulation preservation [17].”
Mimetic finite difference method (2014, methodology): “Mimetic methods with similar properties on triangular meshes are also found in [221] and in [45].”
A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions (2008, methodology): “Detailed discussion on spatial discretizations of various forms of the non-linear convective term (rotational, divergence, skew-symmetric, and advective forms) are provided in [23,26].”
Lagrangian ocean analysis: Fundamentals and practices (2018, background): “, Arakawa 689 A and B), the reconstruction choices include weak-form reconstruction (222), 690 radial basis functions (14), or reconstruction via finite-element basis functions 691 (290).”
A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids (2002, methodology): “To summarize, two key elements are required to produce this fully conservative, secondorder-accurate discretization for nonuniform meshes: (1) the convective term must use the product of the average (midpoint) velocities between the two time levels (this has already been pointed out by Perot [5]) an”
Analysis of an Exact Fractional Step Method (2002, background): “(2), is constructed by discretizing the line integral of the momentum equation at each cell face [19, 20] and constructing a discrete equation for the time evolution of ∫ u · n dl.”
An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator (2006, methodology): “The present formulation differs most significantly with the implementation of the pressure-correction technique and the use of the Eulerian advection of momentum strategy of Perot (2000).”
A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids (2010, methodology): “Perot [23] conducted a similar energy analysis for the incompressible 2D Navier–Stokes equations.”