On the Galerkin formulation of the smoothed particle hydrodynamics method

Cueto‐Felgueroso, Luis; Colominas, Ignasi; Mosqueira, G.; Navarrina, F.; Casteleiro, Manuel

doi:10.1002/nme.1011

Cited by 33 publications

(12 citation statements)

References 31 publications

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“…In the context of using explicit time integration schemes, time stepping stability criteria such as the CFL-condition may be rather restrictive. Moreover, since uncorrected SPH interpolation stencils lack the Kronecker delta property, the application of essential boundary conditions remains nontrivial [46,47].…”

Section: Introductionmentioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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We perform pore-scale resolved direct numerical simulations of immiscible two-phase flow in porous media to study the evolution of fluid interfaces. Using a Smoothed-Particle Hydrodynamics approach, we simulate saturation-controlled primary drainage in heterogeneous, partially wettable 2D porous microstructures. While imaging the evolution of fluid interfaces near capillary equilibrium becomes more feasible as fast X-ray tomography techniques mature, imaging methods with suitable temporal resolution for viscous-dominated flow have only recently emerged. In this work, we study viscous fingering and stable displacement processes. During viscous fingering, pore-scale flow fields are reminiscent of Bretherton annular flow, that is, the less viscous phase percolates through the core of a pore-throat forming a hydrodynamic wetting film. Even in simple microstructures wetting films have major impact on the evolution of fluid interfacial area and are observed to give rise to nonnegligible interfacial viscous coupling. Although macroscopically appearing flat, saturation fronts during stable displacement extend over the length of the capillary dispersion zone. While far from the dispersion zone fluid permeation obeys Darcy's law, the interplay of viscous and capillary forces is found to render fluid flow within complex. Here we show that the characteristic length scale of the capillary dispersion zone increases with the heterogeneity of the microstructure.

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Section: Introductionmentioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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“…) and the derivatives of [17,16,18]. A wide variety of kernel functions appear in the literature, most of them being spline or exponential functions.…”

Section: General Formulationmentioning

confidence: 99%

Finite volume solvers and Moving Least-Squares approximations for the compressible Navier–Stokes equations on unstructured grids

Cueto‐Felgueroso

Colominas²,

Nogueira³

et al. 2007

Computer Methods in Applied Mechanics and Engineering

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This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of high order upwind schemes on unstructured grids, applied to the numerical solution of the compressible Navier-Stokes equations. This meshfree interpolation technique is designed to reproduce arbitrary functions and their succesive derivatives from scattered, pointwise data, which is precisely the case of unstructured-grid finite volume discretizations. The Navier-Stokes solver presented in this study follows the ideas of the generalized Godunov scheme, using Roe's approximate Riemann solver for the inviscid fluxes. Linear, quadratic and cubic polynomial reconstructions are developed using MLS to compute high order derivatives of the field variables. The diffusive fluxes are computed using MLS as a global reconstruction procedure. Various examples of inviscid and viscous flow are presented and discussed.

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“…In the diffuse approach, the derivatives of the shape functions are approximated by the first term in (18) as…”

Section: Diffuse Derivativesmentioning

confidence: 99%

“…Slope limiting was carried out using (74)-(78) with either (79) or (80). First order derivatives are full derivatives (given by (18)), whereas second order derivatives were approximated by the diffuse ones (dropping the succesive derivatives of C C C C C C C C C C C C C C(x x x x x x x x x x x x x x)). The results for the second order scheme with limited gradients are shown in Figure 4.…”

Section: D Dam Break Problemmentioning

confidence: 99%

“…Originally devised for data processing [17], the MLS approximation has become very popular among those researchers working in the class of the so-called meshless or meshfree methods, being widely used both in eulerian and lagrangian formulations. In particular, the authors have recently proposed an algorithm for lagrangian particle hydrodynamics, where the MLS technique played a key role to provide the spatial approximation within an arbitrary cloud of nodes [18]. In this study, second and thirdorder-reconstruction high-resolution schemes, based on Roe's approximate Riemann solver [19], are developed and tested for inviscid and viscous flow applications.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-order finite volume schemes on unstructured grids using moving least-squares reconstruction. Application to shallow water dynamics

Cueto‐Felgueroso¹,

Colominas²,

Fe³

et al. 2005

Int. J. Numer. Meth. Engng

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SUMMARYThis 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 succesive derivatives can be accurately reconstructed using this meshfree technique in a general nodal arrangement. The methodology proposed is used in the construction of low-dissipative highorder high-resolution schemes for the shallow water equations. In particular, second and third-orderreconstruction upwind schemes for unstructured grids based on Roe's flux difference splitting are developed and applied to inviscid and viscous flows. This class of meshfree reconstruction techniques provide a robust and general approximation framework which represents an interesting alternative to the existing procedures, allowing, in addition, an accurate computation of the viscous fluxes. Copyright

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On the Galerkin formulation of the smoothed particle hydrodynamics method

Cited by 33 publications

References 31 publications

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Finite volume solvers and Moving Least-Squares approximations for the compressible Navier–Stokes equations on unstructured grids

High-order finite volume schemes on unstructured grids using moving least-squares reconstruction. Application to shallow water dynamics

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