Simulation of Moving Objects on an Cartesian Mesh Using an Improved Alternating Direction Forcing Immersed Boundary Method

Lead Research Organisation: Imperial College London
Department Name: Aeronautics


The main aim of this PhD project is to develop an improved alternating direction forcing immersed boundary method (AFD IBM) for turbulence-resolving simulations of moving objects on a fixed Cartesian mesh. Most of the immersed boundary methods suffer from spurious force oscillations (SFOs) when moving boundaries are simulated. One of the main sources of SFOs has been identified as the velocity discontinuity that occurs at the immersed boundary interface. The proposed method is based on a cubic spline interpolation to obtain an artificial internal flow within the solid domain while ensuring the continuity of the velocity field at the wall of the solid object. Even though the proposed method is intended for moving objects, it also provides significant improvements for static objects. The ADF IBM will be implemented in the high-order, finite-difference flow solver Incompact3D, which is a powerful tool to simulate turbulent flows using the most powerful supercomputers in the world. Once the ADF IBM is implemented and validated, it will be used to study energy efficient swimming by multiple fish through deep reinforcement learning. By combining state-of-the-art turbulence-resolving simulations of the 3D Navier-Stokes equations with reinforcement learning, this project will demonstrate that fish can reduce their energy expenditure by harnessing turbulence.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 30/09/2016 30/03/2022
2091216 Studentship EP/N509486/1 30/09/2017 29/09/2021 Athanasios Giannenas
Description We developed an original method to simulate turbulent flows with moving objects immersed in the flow. This method will allow the study of drag reduction around bluff bodies using flaps.
Exploitation Route All our methods are open source so the scientific community can use them. We are also open to collaborations. The details of the method are currently under review in a manuscript.
Sectors Aerospace

Defence and Marine



Description Immersed Boundary Method for moving objects 
Organisation University of Poitiers
Country France 
Sector Academic/University 
PI Contribution Contribution from Imperial: Numerical data and expertise in high-fidelity simulations
Collaborator Contribution Contribution from Poitiers: expertise in immersed boundary methods
Impact publication under review.
Start Year 2019
Title Xcompact3d 
Description Xcompact3d is a Fortran-based framework of high-order finite-difference flow solvers dedicated to the study of turbulent flows. Dedicated to Direct and Large Eddy Simulations (DNS/LES) for which the largest turbulent scales are simulated, it can combine the versatility of industrial codes with the accuracy of spectral codes. Its user-friendliness, simplicity, versatility, accuracy, scalability, portability and efficiency makes it an attractive tool for the Computational Fluid Dynamics community. XCompact3d is currently able to solve the incompressible and low-Mach number variable density Navier-Stokes equations using sixth-order compact finite-difference schemes with a spectral-like accuracy on a monobloc Cartesian mesh. It was initially designed in France in the mid-90's for serial processors and later converted to HPC systems. It can now be used efficiently on hundreds of thousands CPU cores to investigate turbulence and heat transfer problems thanks to the open-source library 2DECOMP&FFT (a Fortran-based 2D pencil decomposition framework to support building large-scale parallel applications on distributed memory systems using MPI; the library has a Fast Fourier Transform module). When dealing with incompressible flows, the fractional step method used to advance the simulation in time requires to solve a Poisson equation. This equation is fully solved in spectral space via the use of relevant 3D Fast Fourier transforms (FFTs), allowing the use of any kind of boundary conditions for the velocity field. Using the concept of the modified wavenumber (to allow for operations in the spectral space to have the same accuracy as if they were performed in the physical space), the divergence free condition is ensured up to machine accuracy. The pressure field is staggered from the velocity field by half a mesh to avoid spurious oscillations created by the implicit finite-difference schemes. The modelling of a fixed or moving solid body inside the computational domain is performed with a customised Immersed Boundary Method. It is based on a direct forcing term in the Navier-Stokes equations to ensure a no-slip boundary condition at the wall of the solid body while imposing non-zero velocities inside the solid body to avoid discontinuities on the velocity field. This customised IBM, fully compatible with the 2D domain decomposition and with a possible mesh refinement at the wall, is based on a 1D expansion of the velocity field from fluid regions into solid regions using Lagrange polynomials or spline reconstructions. In order to reach high velocities in a context of LES, it is possible to customise the coefficients of the second derivative schemes (used for the viscous term) to add extra numerical dissipation in the simulation as a substitute of the missing dissipation from the small turbulent scales that are not resolved. Xcompact3d is currently being used by many research groups worldwide to study gravity currents, wall-bounded turbulence, wake and jet flows, wind farms and active flow control solutions to mitigate turbulence. 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact see list of publications