Numerical algorithms for EHL

Elastohydrodynamic lubrication (EHL) concerns the behaviour of a non-Newtonian lubricating fluid which acts to keep two elastically-deformable contacts apart by working against an applied load that is trying to force the contacting elements together. This scenario occurs in a wide variety of important engineering situations and so gaining a thorough understanding of EHL can lead to significant improvements in the efficiency of components such as those occuring in engines and other machinery. The importance of this is obvious in today&#039;s society where improved engine efficiency can lead to energy savings and has major positive environmental implications.<br /> <br /> The aim of this project is to investigate the direct use of nonlinear solution strategies, such as Newton&#039;s method, for this problem. To achieve maximum efficiency preconditioned inner-iterations are required for each step of the nonlinear solver. These must also achieve an optimal efficiency if the overall algorithm is to be competitive with existing solution strategies.<br /> <br /> This work builds on a long history of research in the group which has developed computational algorithms and tools that are used in industry as well as academia.

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Numerical algorithms for EHL&rsquo; as well as&nbsp;<a href="https://engineering.leeds.ac.uk/staff/189/dr_mark_walkley">Dr Mark Walkley</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

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<p><strong>Self-Funding Students are welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the <a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship&nbsp;</a>are available to UK applicants. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK students</strong>&nbsp;&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship&nbsp;</a>&nbsp;is available to support the additional academic fees of international applicants. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

<p>For further information regarding your application, please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:EMAIL@leeds.ac.uk">p</a><a href="mailto:phd@engineering.leeds.ac.uk">hd@engineering.leeds.ac.uk,</a>&nbsp;or by telephone: +44 (0)113 343 5057</p> <p>For further information regarding the project, please contact Dr Mark Walkley by email:&nbsp;&nbsp;<a href="mailto:M.A.Walkley@leeds.ac.uk">M.A.Walkley@leeds.ac.uk</a></p>