Incompressible Navier–Stokes method with general hybrid meshes

Kallinderis, Y.; Ahn, Hyung Taek

doi:10.1016/j.jcp.2005.04.002

Cited by 48 publications

(70 citation statements)

References 37 publications

(59 reference statements)

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“…Haselbacher and Blazek (2000) used virtual edges in order to increase the support of the stencil when prismatic or hexahedral cells are used on a flat solid boundary. Kallinderis and Ahn (2005) used also a volume averaging technique for the computation of velocity gradients at an edge midpoint "   edge   ".…”

Section: Viscous Fluxmentioning

confidence: 99%

“…Kallinderis and Ahn (2005) exploited in 3D an efficient face-wise loop in order to compute the gradients at cells interior. In this way, they avoided redundant visits of each cell face, regarding the evaluation of the divergence theorem surface integral, because a face typically belongs to multiple edge-duals.…”

Section: Viscous Fluxmentioning

confidence: 99%

“…Having the nodal gradients computed, we perform an efficient edge-wise loop in order to compute the gradients at edge midpoints via equation 8. With our method we manage to avoid the complexity of edge-to-cells information of Kallinderis and Ahn (2005) and the use of virtual edges of Haselbacher and Blazek (2000) Additionally we avoid the repetition of the same computations by not visiting the same element (edge-face-cell) multiple times. Furthermore the complete system of Navier-Stokes equations is solved and we do not make any thin-shear layer approximation.…”

Section: Viscous Fluxmentioning

confidence: 99%

“…The term " t  " is the global time-step in physical time. The term " * i   " is the local pseudo-time step for node "i" and for its computation we used an approach originally proposed by Kallinderis (1996) and Kallinderis and Ahn (2005). The equation for…”

Section: Temporal Discretization -Implicit Dual Time-stepping Schemementioning

confidence: 99%

“…Khawaja et al (2000) made use of prismatic, tetrahedral and pyramidal elements. Kallinderis and Ahn (2005) presented an incompressible Navier-Stokes method with general hybrid meshes. Their method was capable of utilizing all four types of three-dimensional elements (i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Vrahliotis

Pappou

Tsangaris

2012

Engineering Applications of Computational Fluid Mechanics

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An unsteady incompressible numerical method for the solution of Navier-Stokes equations is presented. The finite volume solver adopts the method of artificial compressibility, using an implicit dual time stepping scheme for time accuracy. The 2D solver operates on general hybrid meshes containing triangles and quadrilaterals, while the 3D solver operates on hybrid meshes containing tetrahedra, pyramids, prisms and hexahedra. The developed algorithms for spatial discretization and time integration are mesh transparent. An upwind spatial discretization scheme is used for the convective terms and a central scheme for the diffusive terms. Efficient calculation of flow fluxes is implemented in an edge-wise fashion. A new combined method for efficient and accurate evaluation of variable gradients is achieved by using an averaging technique and by avoiding multiple spatial integration of the same element of the mesh. The results obtained agree well with numerical solutions obtained by other researchers.

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Section: Viscous Fluxmentioning

confidence: 99%

Section: Viscous Fluxmentioning

confidence: 99%

Section: Viscous Fluxmentioning

confidence: 99%

Section: Temporal Discretization -Implicit Dual Time-stepping Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Vrahliotis

Pappou

Tsangaris

2012

Engineering Applications of Computational Fluid Mechanics

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An enhanced polygonal finite‐volume method for unstructured hybrid meshes

Ahn

Carey

2006

Numerical Methods in Fluids

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Genuinely multidimensional characteristic‐based scheme for incompressible flows

Razavi

Zamzamian

Farzadi

2007

Numerical Methods in Fluids

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SUMMARYThis paper presents a novel multidimensional characteristic-based (MCB) upwind method for the solution of incompressible Navier-Stokes equations. As opposed to the conventional characteristic-based (CB) schemes, it is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristic structure of incompressible flows modified by artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB scheme in conjunction with the finite-volume discretization is employed to model the convective fluxes. Using this formulation, the steady two-dimensional incompressible flow in a lid-driven cavity is solved for a wide range of Reynolds numbers. It was found that the new proposed scheme presents more accurate results than the conventional CB scheme in both their firstand second-order counterparts in the case of cavity flow. Also, results obtained with second-order MCB scheme in some cases are more accurate than the central scheme that in turn provides exact second-order discretization in this grid. With this inherent upwinding technique for evaluating convective fluxes at cell interfaces, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of MCB scheme lies in its faster convergence rate with respect to the CB scheme that is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed scheme are in good agreement with the standard benchmark solutions in the literature.

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Incompressible Navier–Stokes method with general hybrid meshes

Cited by 48 publications

References 37 publications

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

An enhanced polygonal finite‐volume method for unstructured hybrid meshes

Genuinely multidimensional characteristic‐based scheme for incompressible flows

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