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Laboratory for Scientific Computing


In Computational Fluid Dynamics applications, high-quality mesh generation is a prerequisite for calculating accurate solutions. An attractive alternative to conventional body-fitted or unstructured meshing techniques is offered by the Cartesian cut cell approach. It allows for rapid, automatic, mesh generation for complex geometries, and maintains the computational conveniences offered by the use of Cartesian grids.

The challenge

This Cartesian cut cell approach generates a mesh without the need of optimisation, thus removing a significant bottleneck in the simulation pipeline.


Since the cut cells created at the boundary can be arbitrarily small, they impose a severe constraint on the explicit stable time step for the simulation. The challenge is to overcome this ‘small cell problem’ by designing techniques to evolve the cut cells using the regular cell time-step without sacrificing stability and conservation.

The research

 We adopt a dimensionally split ‘flux stabilisation’ approach to solving the small cell problem. As shown in the figure below, the interface between neighbouring cut cells is divided into ‘unshielded’ and ‘shielded’ regions. Since the unshielded region does not ‘face’ the embedded boundary in the direction of the dimensional sweep, the flux acting on it does not need to be stabilised. Stable explicit fluxes for the shielded regions, on the other hand, are determined by the application of a bespoke conservative one-dimensional flux stabilisation approach. The cut-cell method has been extended by the group to moving boundary flows and compressible Navier-Stokes equations.


 A selection of example results from the Cartesian cut-cell method are shown here. These include the comparison of compressibility effects around high-speed projectiles against experimental Schlieren imaging, a moving boundary axisymmetric open-ended shock tube flow and an implementation of a wall-modelled LES solver for flow around a realistic automotive geometry at 40 m/s.




  • A dimensionally split Cartesian cut cell method for hyperbolic conservation laws, Gokhale N., Nikiforakis, N. and Klein R., Journal of Computational Physics, Volume 364, 1 July 2018, Pages 186–208
  • N. Gokhale, N. Nikiforakis, R. Klein. 2018. A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations, Journal of Computational Physics, Volume 375, pp. 1205–1219
  • A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting., Bennett W.P., Nikiforakis N. and Klein R., Journal of Computational Physics, Volume 368, 1 September 2018, Pages 333–358
  • Cartesian Cut-Cell and GFM Approaches to Free-Surface and Moving Boundary Interaction, Bennett W.P., Michael L., and Nikiforakis N., 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, (AIAA 2016-0602).
  • 3D cut-cell modelling for high-resolution atmospheric simulations, Yamazaki H., Satomura T. and Nikiforakis N. Quarterly Journal of the Royal Meteorological Society, 2016
  • Well-balanced compressible cut-cell simulation of atmospheric flow, Klein R., Bates K.R. and Nikiforakis N., Philos Trans A Math Phys Eng Sci, 367(1907), (2009). 4559-4575.
  • N. Nikiforakis (2009). Theme Issue: Mesh generation and mesh adaptation for large-scale Earth-system modelling. Philosophical Transactions of the Royal Society A, 367 (1907).
  • Slingo, J., Bates, K., Nikiforakis, N., Piggott, M., Roberts, M., Shaffrey, L., Weller, H. (2009). Developing the next-generation climate system models: challenges and achievements. Philosophical Transactions of the Royal Society A, 367, 815-831.
  • "Adaptive mesh refinement for global atmospheric modelling", N. Nikiforakis, Lecture Notes in Computational Science and Engineering, Volume 41, Adaptive Mesh Refinement - Theory and Applications, Tomasz Plewa, Timur Linde and V. Gregory Weirs(editors), Springer Berlin Heidelberg 2005