Composite overlapping meshes for the solution of partial differential equations

Chesshire, G.; Henshaw, William D.

doi:10.1016/0021-9991(90)90196-8

Cited by 476 publications

(344 citation statements)

References 14 publications

Supporting

Mentioning

332

Contrasting

Unclassified

Order By: Relevance

“…Burton & Eaton (2002) also used third-order interpolations, but they interpolated the pressure gradient instead of the pressure. Interpolation of the pressure was used by Chesshire & Henshaw (1990) and Henshaw (1994), who developed discretization methods for collocated overlapping grids.…”

Section: Appendix a Further Specification Of The Numerical Methodsmentioning

confidence: 99%

“…Instead, the overset grid approach used by Burton & Eaton (2005) is adopted and extended to multiple particles: around each particle, a body-fitted (spherical) staggered non-uniform mesh is used, overset on a staggered Cartesian mesh. A finite difference technique that uses multiple overset curvilinear meshes has also been called a composite mesh difference technique (Starius 1977), a chimera grid-embedding technique (Benek, Buning & Steger 1985) and a composite overlapping grid technique (Chesshire & Henshaw 1990;Henshaw 1994). With the overset technique, not only can the number of grid points be limited, but also its body-fitted property facilitates a straightforward computation of the turbulent dissipation rate on the particle surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

View full text Add to dashboard Cite

A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier-Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space-and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller-Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.

show abstract

Section: Appendix a Further Specification Of The Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…As discussed elsewhere (e.g., [19]), Overture uses finite difference approximations on overset grids to discretize the equations on a collection of overlapping, curvilinear grids. This work uses second-order accurate spatial approximations, and the steady-state solution is computed using a pressure-based equation solver [20,21].…”

Section: Computational Fluid Dynamicsmentioning

confidence: 99%

Design Optimization of Vena Cava Filters: An Application to Dual Filtration Devices

Singer

Wang

Diachin³

2010

Journal of Biomechanical Engineering

View full text Add to dashboard Cite

Background: Pulmonary embolism (PE) is a significant medical problem that results in over 300,000 fatalities per year. A common preventative treatment for PE is the insertion of a metallic filter into the inferior vena cava that traps thrombi before they reach the lungs. The goal of this work is to use methods of mathematical modeling and design optimization to determine the configuration of trapped thrombi that minimizes the hemodynamic disruption. The resulting configuration has implications for constructing an optimally designed vena cava filter.Approach: Computational fluid dynamics is coupled with a nonlinear optimization algorithm to determine the optimal configuration of trapped model thrombus in the inferior vena cava. The location and shape of the thrombus are parameterized, and an objective function, based on wall shear stresses, determines the worthiness of a given configuration. The methods are fully automated and demonstrate the capabilities of a design optimization framework that is broadly applicable.Results: Changes to thrombus location and shape alter the velocity contours and wall shear stress profiles significantly. For vena cava filters that trap two thrombi simultaneously, the undesirable flow dynamics past one thrombus can be mitigated by leveraging the flow past the other thrombus. Streamlining the shape of thrombus trapped along the cava wall reduces the disruption to the flow, but increases the area exposed to abnormal wall shear stress. Conclusions:Computer-based design optimization is a useful tool for developing vena cava filters. Characterizing and parameterizing the design requirements and constraints is essential for constructing devices that address clinical complications. In addition, formulating a well-defined objective function that quantifies clinical risks and benefits is needed for designing devices that are clinically viable.

show abstract

“…Two important areas are the extension of the approach to variable coefficients and to systems of second-order wave equations such as Maxwell's equations written in second-order form [11], or the elastic wave equation and nonlinear extensions thereof. To address geometric complexity we will develop approximations for curvilinear grids which can be used in the context of overlapping grids [20] to develop efficient schemes for complex geometry. As shown in [10] for the case of the first-order system for linear elasticity, upwind schemes can be very effective when solving wave-propagation problems on overlapping grids since they naturally suppress possible instabilities that can be generated from the overlapping grid interpolation.…”

Section: Discussionmentioning

confidence: 99%

Upwind schemes for the wave equation in second-order form

Banks

Henshaw

2012

Journal of Computational Physics

View full text Add to dashboard Cite

We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d'Alembert's exact solution. We construct conservative finite difference approximations, although finite volume approximations are also possible. High-order accuracy is obtained using a space-time procedure which requires only two discrete time levels. The advantages of our approach include efficiency in both memory and speed together with accuracy and robustness. The stability and accuracy of the approximations in one and two space dimensions are studied through normal-mode analysis. The form of the dissipation and dispersion introduced by the schemes is elucidated from the modified equations. Upwind schemes are implemented and verified in one dimension for approximations up to sixth-order accuracy, and in two dimensions for approximations up to fourth-order accuracy. Numerical computations demonstrate the attractive properties of the approach for solutions with varying degrees of smoothness.

show abstract

Composite overlapping meshes for the solution of partial differential equations

Cited by 476 publications

References 14 publications

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Design Optimization of Vena Cava Filters: An Application to Dual Filtration Devices

Upwind schemes for the wave equation in second-order form

Contact Info

Product

Resources

About