A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations

Gokhale, Nandan; Nikiforakis, Nikolaos; Klein, Rupert

doi:10.1016/j.jcp.2018.09.023

Cited by 4 publications

(2 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since we are studying an incompressible system, we also require the solution of Poisson equations, which was published by Johansen and Colella in 1998 13 ; a feat which they and McCorquodale naturally extended to solutions of the heat equation a few years later 14 . Developing novel and improved schemes for embedded boundaries is still an active area of research [15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

Sverdrup,

Almgren,

Nikiforakis

2019

Preprint

View full text Add to dashboard Cite

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialised treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretisation, in which viscous terms are treated semi-implicitly and projection methods are utilised to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.

show abstract

Section: Introductionmentioning

confidence: 99%

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

Sverdrup,

Almgren,

Nikiforakis

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In unfitted boundary methods the moving domain is instead embedded in a fixed grid. The methods of this class are based either on FEM, such as XFEM [36,50] or GFEM [13], on meshless methods [57], or Cartesian meshes, such as cut cell methods [33].…”

Section: Introductionmentioning

confidence: 99%

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

Coco

2019

Preprint

View full text Add to dashboard Cite

In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted boundary methods, since the mesh does not adapt to the moving boundary. The equations are advanced in time by using Crank-Nicholson. The momentum and continuity equations are solved simultaneously for the velocity and the pressure by adopting a proper multigrid approach. To avoid the checkerboard instability for the pressure, a staggered grid is adopted, where velocities are defined at the sides of the cell and the pressure is defined at the centre. The lack of uniqueness for the pressure is circumvented by the inclusion of an additional scalar unknown, representing the average divergence of the velocity, and an additional equation to set the average pressure to zero. Several tests are performed to simulate the motion of an incompressible fluid around a moving object, as well as the lid-driven cavity tests around steady objects. The object is implicitly defined by a level-set approach, that allows a natural computation of geometrical properties such as distance from the boundary, normal directions and curvature. Different shapes are tested: circle, ellipse and flower. Numerical results show the second order accuracy for the velocity and the divergence (that decays to zero with second order) and the efficiency of the multigrid, that is comparable with the tests available in literature for rectangular domains without objects, showing that the presence of a complex-shaped object does not degrade the performance.

show abstract

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

Coco

2020

Journal of Computational Physics

View full text Add to dashboard Cite

A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations

Cited by 4 publications

References 40 publications

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

Contact Info

Product

Resources

About