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  Development of physics-constrained reduced order models of thermally driven flows

   Department of Mechanical and Aerospace Engineering

  ,  Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

Project description

Thermally driven turbulent flows in engineering and geophysical systems, are highly dimensional, nonlinear, and multi-scale. The numerical simulation of such flows is extremely computationally expensive. It is, therefore, not possible to undertake enough of these simulations to span the range of plausible operating conditions.

This project focusses on the development of physics-constrained reduced order models (ROM) that reproduce the statistical properties of numerically simulated thermally driven turbulence, at a fraction of the computational cost. This fundamental research would enable the sensitivity analysis and robust design of many applications including: energy generation systems; heating, ventilation and cooling; and climate change response under varying degrees of future greenhouse gas forcing.

Whilst such turbulent flows are chaotic, they still comprise of large-scale three-dimensional coherent structures with significant temporal and spatial correlations. Our ability to understand and predict these flows will benefit from reducing these systems to their most basic building blocks. One might consider reduced order modelling as being the mathematical representation of an adage attributed to Einstein that, “a model should be as simple as possible, but no simpler”.  

As opposed to typical black-box methods, we focus on approaches inherently constrained by the physics. Specifically, models derived from the Galerkin projection of the equations of motion onto an appropriate basis learnt from the underlying data (e.g. proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), etc.). This basis defines our “building blocks”. The projection approach ensures the model is interpretable, and potentially also more representative for simulating out-of-sample conditions, not previously observed in the data.

Reduced order modelling of thermally driven flows is not only key to understanding climate sensitivity, but also key to the design of potential engineering solutions to mitigate and adapt to a changing environment. The outcomes of this project will be of interest to many stakeholders across academia, industry and government in Australia and beyond. Delivering upon this project will, therefore, open many doors to the student, following the successful completion of their PhD.

PhD student role description

The role of the PhD students and their contribution to the project is to develop and validate reduced order modelling approaches to the simulation of highly dimensional thermally driven turbulent flows. They will undertake computational fluid dynamics simulations to generate initial test cases of canonical thermally driven turbulence. They will calculate a series of different flow decompositions (e.g. POD, DMD, etc.). They will extend existing codes for the calculation of the reduce order model coefficients using optimisation methods and test a variety of normalisations and regularisation approaches. Upon successful demonstration of the approach, the students will be given the opportunity to generate ROMs of higher dimension thermally driven flow databases previously generated by the group, following their research interests (e.g. thermal turbulent boundary layer, global atmosphere and/or ocean).

The PhD students will be part of an interdisciplinary team undertaking research in the fields of turbulent thermo-fluids, direct numerical simulation of turbulent shear flows, global climate simulations, scientific high-performance computing, data assimilation, reduced order modelling, and scientific machine learning. This research collaboration spans PhD students, post-docs and more senior researchers at Professor Soria group at Monash University in the Mechanical Engineering and Aerospace Department, and Dr Kitsios’ colleagues at the CSIRO Environment department.

Required skills and experience

The candidates must have outstanding knowledge in Mathematics and/or the theory of Fluid Mechanics.

Experience in programming (e.g. in Python, Julia, C/C++ or F90) is essential.

Knowledge of MPI and/or MP is desirable.

Experience in numerical simulations and/or machine learning is necessary.


Eligibility and application process

Two positions are available.

You will have to be awarded the necessary Monash University scholarships to undertake a PhD under the co-supervision of Prof. Soria and Dr Kitsios. Details can be found at:

An additional top-up scholarship of up to $10,000 per year is also available to exceptional candidates based on a successful interview. 

A step-by-step guide to applying for admission/scholarships at Monash University can be found at: 

Note that the process starts with you submitting an "Expression of Interest”, only after we (Prof Soria & Dr Kitsios) have given provisional email approval for you to do so. This is followed by you receiving and “Invitation to apply” from the Faculty of Engineering. Further details on the Expression of Interest can be found at:

Due to international visa processing times and the project timeline, we encourage candidates from only the following regions to apply: Australasia; Europe; and the Americas.

The closing date for the international student scholarships is August 30 and March 31 each year.

The closing date for domestic (Australian permeant residents, citizens and NZ citizens) student scholarships is October 31 and May 31.

Contact Prof. Soria () and Dr Kitsios (, ) for further information.

Engineering (12) Environmental Sciences (13) Mathematics (25) Physics (29)

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