Software development for reaction-diffusion modelling

Reaction-diffusion processes form an essential component of many problems in molecular and systems biology. Software tools to simulate these processes are becoming increasingly important as computational capability grows, allowing problems previously intractable (such as whole cell simulation) to become feasible. To enable these large-scale simulations, a multiscale description is necessary so that the software can accurately and efficiently use reaction-diffusion models with different levels of detail in different parts of the computational domain.

Ion Channel
Ca2+ Intracellular Signalling


  1. Martin Robinson, Mark Flegg and Radek Erban (2013), Adaptive two-regime method: application to front propagation, Submitted to Journal of Chemical Physics. preprint

Dispersion of a granular bed by a liquid jet

The dispersion of a granular bed by a liquid jet is of broad relevance to the food processing industry. A current project with Prof. Stefan Luding from U Twente and Dr. Marco Ramaioli from Nestlé Research Centre involves the simulation of this system using SPH-DEM and comparison with experimental high speed camera and MRI data.

Dispersion Cell Experiments
SPH-DEM Simulation


  1. Martin Robinson, Stefan Luding, Marco Ramaioli (2013) SPH-DEM simulations of grain dispersion by liquid injection, Powders and Grains 2013, Sydney pdf / proceedings

Mesoscale fluid-particle simulation using SPH-DEM

Fluid-particle systems are ubiquitous in nature and industry. Sediment transport and erosion are important in many environmental studies and the interaction between particles and interstitial fluid affects the rheology of avalanches, slurry flows and soils. In industry, the dispersion of solid particles in a fluid is also of broad relevance in the food, chemical and painting industries. .

We present a meshless fluid-particle simulation method using two-way coupled Smoothed Particle Hydrodynamics and Discrete Element Method (SPH-DEM) formulation. In contrast to similar methods in the literature, this is a purely particle-based solution method and therefore enjoys the flexibility that is inherent in these methods. The SPH-DEM model is applied to 3D test problems involving single and multiple particle sedimentation in a water column.

Single Particle Sedimentation Results
Rayleigh Taylor Instabilty


  1. Martin Robinson, Stefan Luding and Marco Ramaioli, (2014). Fluid-particle flow modelling and validation using two-way-coupled mesoscale SPH-DEM, Int. Journal of Multiphase Flow, 59:121-134. preprint / journal page
  2. Martin Robinson, Marco Ramaioli, Stefan Luding (2013) Grain Sedimentation with SPH-DEM and its Validation, Powders and Grains 2013, Sydney pdf / proceedings
  3. Mohammadreza Ebrahimi, Prashant Gupta, Martin Robinson, Martin Crapper, Marco Ramaioli, Jin Y. Ooi (2013) DEM-CFD and SPH-DEM methods in single and multiple particle sedimentation test cases, III International Conference on Particle-based Methods – Fundamentals and Applications PARTICLES 2013
  4. Martin Robinson, Marco Ramaoli, (2011). Mesoscale fluid-particle interaction using two-way coupled SPH and the Discrete Element Method, SPH European Research Interest Community (SPHERIC) workshop

Simulation and Analysis of Chaotic Mixing

We use Smoothed Particle Hydrodynamics (SPH) simulations to better understand the mixing performance of a range of industrial mixers. The chaotic manifolds of the flow are used to describe the mixing and to identify isolated regions. We present a method for calculating the Finite-Time Lyapunov Exponent (FTLE) using SPH particle data in two and three dimensions. The FTLEs can be used to locate the unstable and stable manifolds in the flow and indicate where mixing is either promoted or inhibited in the flow. This is combined with a quantitative mixing measure that calculates the degree of mixing between different regions. This research shows that examining the chaotic manifolds within a typical industrial mixer can provide valuable insight into both the transient and long-term mixing processes, leading to a more focused exploration of possible mixer configurations and to practical improvements in mixing efficiency.

This mixing simulation and analysis method is applied to the following applications:

  • 2D Twincam mixer
  • 3D Helical Ribbon Mixer
  • 3D Twin Screw Extruder
Twincam Mixer Twinscrew Extruder
Helical Ribbon Mixer


  1. Martin Robinson and Paul Cleary, (2012). Flow and Mixing Performance in Helical Ribbon Mixers. AIChE Journal, in review
  2. Paul Cleary, Martin Robinson, (2011) Understanding viscous fluid transport and mixing in a twin screw extruder, 8th International Conference on CFD in the Oil & Gas, Metallurgical and Process Industries
  3. Martin Robinson and Paul Cleary, (2011). The influence of cam geometry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer. AIChE Journal, 57:581-598.
  4. Martin Robinson, Paul Cleary, Joe Monaghan, (2008). Analysis of mixing in a Twin-Cam mixer using Smoothed Particle Hydrodynamics, AIChe Journal, 54(8):1987-1998.

DNS Simulations of 2D Turbulence using SPH

We explore the application of SPH to a Direct Numerical Simulation (DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain. In this bounded domain, the inverse energy cascade, and a net torque exerted by the boundary, result in a spontaneous spin up of the fluid, leading to a typical end state of a large monopole vortex that fills the domain. The SPH simulations were compared against published results using a high accuracy pseudo-spectral code.

The purpose of this research is to provide information on how well SPH models turbulent flow without the additional complication of a turbulence model. While there have been many SPH turbulence models presented in the literature, these have not shown a clear advantage over standard SPH, and there is some speculation that the method naturally contains an artificial LES-type model. It is therefore important to explore how well standard SPH can simulate various classes of turbulent flow, in order to determine the suitability of the method to turbulence applications and to provide results that can inform the development of any future SPH turbulence models.

Vorticity Plot of Forced 2D Turbulence
Kinetic Energy Spectrum of Forced 2D Turbulence


  1. Martin Robinson and Joseph J. Monaghan, (2011). Direct numerical simulation of decaying two-dimensional turbulence in a no-slip square box using smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids. doi: 10.1002/fld.2677
  2. Martin Robinson, Joe Monaghan, (2008). Forced two-dimensional wall-bounded turbulence using SPH, SPH European Research Interest Community (SPHERIC) workshop, Lausanne.
  3. Martin Robinson, Joe Monaghan, John Mansour, (2007). DNS SPH simulation of 2D wall- bounded turbulence”, SPH European Research Interest Community (SPHERIC) workshop, Madrid.

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