# Adaptive Numerical Algorithms for Forward UQ in Time-Dependent CFD.

• Applications accepted all year round
• Funded PhD Project (UK Students Only)

## Project Description

Uncertainty quantification (UQ) is a rapidly-evolving field, incorporating several traditional mathematical disciplines. This project will develop new adaptive numerical algorithms for the forward propagation of uncertainty in large-scale time-dependent CFD (computational fluid dynamics) simulations and is a collaboration between the School of Mathematics at the University of Manchester and IBM Research UK. The project will be jointly supervised by Dr. Catherine Powell and Professor David Silvester from the School of Mathematics, and Dr. Malgorzata Zimon from IBM Research UK. The PhD student will be based in the School of Mathematics but will also have the opportunity to spend a minimum of 3 months working alongside researchers at IBM Research UK’s premises in Daresbury.

In real-world applications, when using mathematical models to simulate real-world processes (such as fluid flows) we frequently encounter situations where we are uncertain about one or more of the inputs (viscosity, material parameters, initial conditions, geometry etc). In forward UQ, the main aim is to assess the impact of uncertainty in the model inputs on quantities of interest associated with the model’s outputs. For this, we require computationally efficient numerical methods that can take in a probability distribution for the model’s inputs and deliver accurate approximations of statistical quantities of interest related to the model’s outputs. For time-dependent problems, and especially those with non-smooth solutions, the approximation space often needs to be adapted in time to maintain accuracy. How to design adaptive numerical algorithms with guaranteed error control is highly challenging.

Candidates with a strong background in applied mathematics and numerical analysis with a passion for solving real-world problems efficiently on computers are encouraged to apply. Some prior experience in scientific computing (Python, MATLAB, C or Fortran etc) is desirable but not essential. Applicants should have (or be on track to to be awarded) either (i) a first class honours MMath degree or (ii) a first class honours BSc degree in Mathematics and a one-year MSc degree in a relevant mathematical discipline.

In the first instance, applicants should supply a cover letter describing their academic background and motivation for the project, as well as a complete CV (two pages maximum). These will be considered upon receipt and suitable applicants then encouraged to submit a formal application.

## Funding Notes

For eligible UK applicants, funding is available to cover tuition fees and annual maintenance payments at the standard EPSRC rate, plus a top-up from the sponsor. For eligible EU applicants, funding is only available to cover tuition fees.

## How good is research at University of Manchester in Mathematical Sciences?

FTE Category A staff submitted: 54.40

Research output data provided by the Research Excellence Framework (REF)

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