Parallel implementation of numerical modelling of concentration polarisation and cake formation in membrane filtration processes
Bun Lo  1, *@  , Oubay Hassan  1@  , Jason Jones  1@  
1 : Swansea University
Swansea University, Bay Campus, Fabian Way, Swansea. SA1 8EN -  United Kingdom
* : Corresponding author

Filtration processes are the centrepiece in many water treatment techniques, including waste water treatment and desalination. In finding an optimal setup for such processes, computational simulations are more economical and efficient than performing experiments. With modern computers having multicore CPUs, and GPUs capable of general computation, sequential codes are unable to harness the computational power available and must be converted to a parallel version.

An existing model capable of predicting concentration polarisation and cake formation in crossflow membrane filtration is implemented on different parallel platforms. The governing equations, Navier Stokes equations for the hydrodynamics and convection diffusion equation for suspended particles, are solved numerically using the lattice Boltzmann method. The equations are coupled through velocity, viscosity and diffusion coefficient, which are assumed to vary with the solute concentration.

A sequential algorithm for this model was analysed to identify potential parallelisation sections and implemented in C++ with OpenMP for multicore CPU, MPI for multiple CPUs and CUDA for GPUs. After converting to parallel algorithms, bottlenecks were identified and appropriate optimizations were applied according to the language and hardware used. In general, these optimizations aim to fully utilise pipelines concurrently and eliminate unnecessary workload.

The parallelised algorithms are validated by comparing the results obtained for a number of problems with the predictions produced by other computational models and experimental results available in literature. With the current setup, the algorithms are both memory bound and compute bound, which allow them to scale well with increasing number of computing units. The paper will demonstrate the bottlenecks, effectiveness of optimizations and the performance of the parallel codes.

The parallel implementation of the modelling process demonstrates the potential of the computational technique to be deployed for the prediction of concentration polarisation and cake formation in a fast and efficient manner. Simulations can be done with higher resolution in a much faster timeframe, which allows better optimization of membrane filtration processes. 

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