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Oliver Dunbar

About Me:

Myself x3

Originally from Aylesbury, Buckinghamshire, I took my undergraduate studies at the University of Bath where I completed my MMath. As part of MASDOC I have completed an MSc in Mathematics and Statistics and I have now completed my PhD in Mathematics.

My current position is as a postdoctroal research fellow under the EQUIP grant.

My current interests are in the deterministic and probabilistic solution to PDE based inverse problems. In particular, my directions lie in solutions of the inverse Eikonal equation, and the application of this to first traveltime tomography problems in geophysics.

My PhD resided in applied analysis and numerics. The analysis I am studied was a diffuse interface (phase field) model of multiphase fluids to answer questions of whether this mathematical approach can still capture accurate behavioural properties, especially regarding phenomena along interfaces such as the effects of surfactants. I have written a scheme to model these systems in the DUNE-FEM toolbox, which I have shown is second order accurate with variable and fixed density flow, and demonstrated stability.

Prior to this , my MSc year of the MASDOC program included projects in multiscale crystal modelling and in numerical methods for moving surface PDE systems. My fourth year project in Bath - titled "Optimal Transport and its Applications" - was completed under Professor Chris Budd.

Personal/Professional Details:

These can be found in this Brief Academic CV, (you can request my full CV via email)

...or visit my LinkedIn profile.

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MASDOC: PhD Third Year 2016-17

Current Research: Diffuse interface modelling of multiphase fluid with surfactant.

A brief overview of my research is given by these slides. (Note: animations will not play in online PDF reader). These are for a more general PhD audience. Other more recent work I have completed involves the code for a fully coupled Surfactant-Cahn-Hilliard-Navier-Stokes system, which has passed several quantitative and qualitative test scenarios.

Some videos of the code I have written in its full glory will be uploaded to this youtube channel.

I am currently studying the numerical analysis of Cahn-Hilliard Navier-Stokes system, in particular I am considering the coupling's numerical stability within the framework of a fractional theta splitting scheme for the Navier Stokes system. This allows decoupling of the incompressibility and convection of the Navier stokes, and I have created a coupled scheme for fixed and variable density flows that remains second order in time, i have shown stability results for fixed density and will repeat the analysis for variable density flows soon.

Talks/Poster presentations:

Warwick Postgraduate Seminar, 30th November, Talk Title: "From Soap to Simulation: A phase field story",

Micro and Nanoflows Workshop, 15th December, Talk Title: "Phase field modelling for surfactants in a multifluid"

Teaching:

Class Teacher for Analysis 1,

Teaching Assistant for (MASDOC) C1 Module

SIAM:

I am the treasurer (outgoing in 2017) of the SIAM Warwick student chapter. For information on SIAM student chapters, click here. For upcoming Warwick events, see our facebook page. Our latest events were two SIAM conferences on Statistics & Machine Learning and on Applied Maths, details found here.

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MASDOC: PhD Second Year 2015-16


Modules Taken:

Taught Course Centre: The Basis of the Mathematical Theory of Compressible Viscous Flow, Dr. E. Zatorska

Talks/Poster presentations:

SIAM Student conference, 25th November, Talk title "From Soap to Simulation: Surfactant Flow in a Multi-fluid",

Scientific Computing Research Showcase, 2nd February, Poster title "From Soap to Simulation",

MASDOC Retreat, 24th May, Talk title "From Soap to Simulation: A Diffuse Model of Surfactant Flow in a Multi-fluid"

SIAM National Student Chapter conference, 27th May, Talk title "From Soap to Simulation: A Diffuse Model of Surfactant Flow in a Multi-fluid"

(Note: the talks were different but the titles the same!)

Teaching:

Class Teacher for Analysis 1,

Supervisor for two groups of 2nd year mathematics students,

Teaching Assistant for Analysis 2

SIAM:

I am the current treasurer of the SIAM Warwick student chapter. For information on SIAM student chapters, click here. For upcoming Warwick events, see our facebook page.

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MASDOC: PhD First Year 2014-15


Modules Taken:

CY901- High Performance Scientific Computing, Dr. David Quigley

MA4E3 - Asymptotic Methods, Dr. Claude Baesens

Taught Course Centre: Non-Linear PDE's and Applications, Prof. José Carillo

Talks/Poster presentations:

Applied PDEs seminar, 18th November and Postgraduate seminar, 26th November. Talk title "Knot energies in the numerical detection of self-intersecting moving membranes"

Computing Matters Workshop, 23rd January. Poster title "Model coupling and Applications"

MASDOC-CCA joint conference, 17th April. Talk title "A diffuse interface model of a multi phase fluid with surfactant"

MASDOC Retreat, 20th May, Young Reasearchers in Mathematics conference, 19th August, Talk title "A diffuse interface model of a multi phase fluid with surfactant”

Other Conferences Attended:

BMC/BAMC/LMS Conference (University of Cambridge, Apr 2015)

Shapes and Patterns, Analysis and Simulation Seminar (Mathematische Forschungsinstitut Oberwolfach, May 2015)

Mathematical Thermodynamics of complex fluids Summer School (Fondazione CIME, Cetraro, June 2015)

Teaching:

Supervisor for two groups of 2nd year mathematics students,

TA for Analysis 3 and for Analysis 2.

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MASDOC: Msc Year 2013-14

Modules Taken:

MASDOC modules: A1,A2,C1,C2,P1,P2

Research Study Group: Model Coupling and Applications

Authors: O. , Yulong Lu, Luke Williams

Supervisors: Dr. Andreas Dedner, Prof. Christoph Ortner

MCA Webpage , MCA Project

Summer Research Project: Knot energies in the numerical detection and prevention of self-intersecting moving membranes

Supervisors: Dr. Björn Stinner, Dr. Andreas Dedner

SRP Proposal , SRP Project

Conference Attendance:

BMS summer school: Applied Analysis for Materials (FU Berlin, Aug-Sep 2014)

Young Researchers in Mathematics Conference (University of Warwick, Aug 2014)

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