Using HPC to Advance Water Desalination By Electrodialysis
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The document discusses the use of high-performance computing (HPC) to enhance water desalination through electrodialysis, specifically highlighting the development of Ekaos, a direct numerical simulation code. It compares the efficiencies of commercial software versus custom codes, emphasizing Ekaos's speed and lack of artificial smoothing, which better captures complex fluid behaviors. The findings suggest that while 2D and 3D simulations of electroconvective chaos show qualitative similarities, they also reveal quantitative differences in predicting current density.
Using HPC to Advance Water Desalination By Electrodialysis
- 1. Using HPC To Advance Water Desalination By Electrodialysis Clara Druzgalski Department of Mechanical Engineering Stanford University
- 3. Electrodialysis: Industrial Electrodialysis water treatment plants in Barcelona, Spain produce 257 million liters of water per day. Abrera (2007) 200 million liters Sant Boi del Llobregat (2009) 57 million liters Credit: Sant Boi del Llobregat
- 4. Electrodialysis: Applications GrayWhite Black Portable water treatment Salt production Biomedical analysis: lab-on-a-chip devices
- 6. Model Problem Channel Height 10-6 meters Smallest Feature 10-9 meters Applied voltage 1-3 Volts Example Dimensional Values
- 7. Model Problem: Experiments Well-described by 1D theory Electroconvective chaos: 1D theory no longer predictive
- 8. “ Should we use a commercial code like Comsol Multiphysics or build a high performance code from scratch? ?
- 9. Commercial Software Commercial codes often use artificial smoothening for numerical robustness. This dissipates small structures generated by turbulent and chaotic fluid motion. Commerical codes must be general enough to handle a wide variety of problems, but this limits the user’s ability to take advantage of crucial time-saving algorithms
- 11. Custom HPC Software EKaos a high performance direct numerical simulation code that simulates electrokinetic chaos. No artificial smoothening Over 100 times faster than Comsol on a single node in 2D.
- 12. EKaos
- 13. 2D EKaos Simulation Concentration Charge Density
- 14. Experimental Observation Joeri C. de Valença, R. Martijn Wagterveld, Rob G. H. Lammertink, and Peichun Amy Tsai Phys. Rev. E 92, 031003(R) – Published 8 September 2015
- 15. Simulation vs. Experiment Experiment: De Valenca, et. al. Simulation: Davidson, et. al. Submitted to Scientific Reports
- 17. 2D EKaos: Current-Voltage Qualitative matching with experiment 17
- 19. 165 million mesh points That’s over 1 billion degrees of freedom 11 terabytes of data Per simulation 100,000 time steps To reach converged statistics Each 3D EKaos simulation…
- 20. “ Why is a simulation of just one small section of a desalination channel so computationally expensive? ? The computational cost is determined by the range of relevant length and time scales that must be resolved.
- 21. Algorithm Details The mathematical details behind a high performance code
- 22. Governing Equations Species Conserva.on: Navier-Stokes: Gauss’s Law: c+ Concentration of cation c- Concentration of anion ϕ Electric potential u Velocity vector P Pressure 22 y x
- 24. Dimensionless Parameters Parameter Description Range Value ϵ Screening length, EDL size 10-6 – 10-3 10-3 Δϕ Applied voltage 20-120 120 κ Electrohydrodynamic coupling const. O(1) 0.5 c0 + Cation concentration at membrane >1 2 Sc Schmidt number 103 103 24
- 25. Spatial Discretization 25 EKaos: 2D and 3D Direct numerical simulation (DNS) 3D has over 165 million spatial grid points Staggered mesh configuration Non-uniform mesh is used in the membrane-normal direction to handle sharp gradients Discretization: 2nd order central finite difference scheme
- 30. Time Integration Equa.on in δ-form Remove Direc.onal Coupling Move non-s.ff terms to leQ hand side 30
- 31. Time Integration Equa.on in δ-form Remove Direc.onal Coupling Move non-s.ff terms to leQ hand side 31
- 32. Time Integration Equa.on in δ-form Analy.cal subs.tu.on using Gauss’s Law Remove Direc.onal Coupling
- 33. Time Integration Final Equa.on • LeQ hand side operator is linear and now only involves local coupling between δc+ and δc- • We need to solve for u*, v*, w*, P*, and ϕ* at each itera.on 33
- 35. By taking advantage of the geometry and using physical insight we were able to: 1. Design operators that reduced the matrix bandwidth 2. Use fast and robust math libraries such as LAPACK and FFTW 3. Reduce communication cost across processors by designing the algorithm with parallelization in mind.
- 36. Conclusions Developed EKaos: a parallel 3D DNS code to simulate electroconvective chaos. Developed a numerical algorithm for efficiently solving the coupled Poisson-Nernst-Planck and Navier-Stokes equations Improved prediction of mean current density that has been observed in experiments Comparison of 2D and 3D simulations show qualitative similarities, but quantitative differences Electroconvective chaos can generate structures similar to turbulence. 36
- 37. Thanks! Any questions? You can find me at: [email protected]