PhD Studentship: Hybrid Explicit-implicit Time Integration Schemes for Smoothed Particle Hydrodynamics

4 weeks ago


Manchester, United Kingdom The University of Manchester Full time

This is a 3.5 year PhD Studentship which will cover fees and stipend set at the UKRI rate (£18,622 in 2023/24). This project is open to UK residents and EU residents who have settled status or pre-settled status.

The successful candidate will have strong mathematical background, especially in numerical analysis. Knowledge of differential equations is an advantage. Strong programming skills in C++ and Fortran are essential.

Smoothed particle hydrodynamics (SPH) is a method for numerical solution of fluid mechanics problems. In this method fluid continuum is approximated by a number of interacting particles. The position and the velocity of each particle in time is determined from the kinematic relations with the neighbouring particles. This procedure leads to the problem of solving of a system of initial value problems (IVPs).

There are two classes of methods for numerical solution of IVPs: explicit and implicit. Explicit methods are simple to implement and are computationally cheaper per time step than implicit methods. However, explicit methods suffer from instability that restricts severely the maximum allowed step size. Implicit methods are unconditionally stable, allowing to select step sizes that follow the physics of the problem under consideration, rather than method-imposed restrictions. The computational cost of implicit methods is higher than that of explicit methods and needs to be managed carefully.

The choice of a time integration scheme is inevitably problem-dependent. Many complex fluid mechanics problems exhibit multiple time scales, and the use of a single time integration scheme over the entire time interval of interest may not be the best possible choice. Instead, we should build a flexible framework that would facilitate the design of hybrid explicit-implicit time integrators for SPH. The objective of this project is to design and implement a prototype of such a system. There are two main components of this system: 1) a computational cost model for explicit and implicit methods as the basis of a decision making which type of integrator to use, and 2) the investigation of different methods for numerical estimation of the local truncation error. The system will be thoroughly tested on standard benchmarks before being deployed within the SPH method to solve more realistic problems.

We strongly recommend that you contact the supervisor(s) for this project before you apply; The Email addresses for Dr Milan Mihajlovic and Dr Georgios Fourtakas are and


  • PhD STUDENTSHIPS

    3 weeks ago


    Manchester, United Kingdom Cancer Research UK Manchester Institute (CRUK MI) Full time

    "Blocking proteins as a novel approach to treat blood cancer"Research Group Leukaemia BiologyCancer Research UK Manchester InstituteCRUK 4 Year PhD Studentships 2024This 4-year PhD studentship will be based at the Cancer Research UK Manchester Institute, New Paterson Building, Withington, Manchester, UKWhile there has been substantial progress in the...

  • PhD STUDENTSHIPS

    2 weeks ago


    Manchester, United Kingdom Cancer Research UK Manchester Institute (CRUK MI) Full time

    4 Year PhD Studentship - Autumn 2024Cancer Research UK Manchester InstituteProject Title: "Blocking proteins as a novel approach to treat blood cancer" Research Group: Leukaemia BiologyGroup Leader: Tim SomervailleThis 4-year PhD studentship will be based at the Cancer Research UK Manchester Institute, New Paterson Building, Withington, Manchester, UKWhile...


  • Manchester, United Kingdom The University of Manchester Full time

    Application deadline: 31/07/2024Research theme: Offshore renewable energy; water wavesHow to apply: Please click the 'Apply' button, above.The design of offshore renewable energy systems should consider realistic ocean extremes which can be complex and highly nonlinear. However, linear models are often used for design due to their low cost, resulting in...


  • Manchester, United Kingdom The University of Manchester Full time

    Application deadline: 31/07/2024 Research theme: Offshore renewable energy; water waves How to apply: Please click the 'Apply' button, above. The design of offshore renewable energy systems should consider realistic ocean extremes which can be complex and highly nonlinear. However, linear models are often used for design due to their low cost, resulting in...


  • Manchester, United Kingdom The University of Manchester Full time

    Applications are invited for the position of Lecturer in Particle Physics on the LHCb experiment. Lecturer is a permanent academic staff member equivalent to assistant professor in the US naming convention. We are seeking to appoint a particle physicist with an excellent track record of research and publications. You are invited to bring and lead your own...


  • Manchester, United Kingdom The University of Manchester Full time

    This is a 3.5 year PhD Studentship which will cover fees and stipend set at the UKRI rate (£18,622 in 2023/24). This project is open to UK residents and EU residents who have settled status or pre-settled status.The successful candidate will have a good degree in mathematics, physics, engineering, environmental sciences, or similar, with good understanding...


  • Manchester, United Kingdom The University of Manchester Full time

    Applications are invited for the position of Lecturer in Particle Physics on the LHCb experiment. Lecturer is a permanent academic staff member equivalent to assistant professor in the US naming convention.We are seeking to appoint a particle physicist with an excellent track record of research and publications. You are invited to bring and lead your own...


  • Manchester, United Kingdom Manchester Metropolitan University Full time

    Project summaryRehabilitation services prove highly effective in managing numerous chronic conditions such as coronary artery disease, yet they remain underutilized among patients. Further, disparities in care are evident as the data indicates that women and individuals from socioeconomically deprived areas are notably less likely to attend rehabilitation,...


  • Manchester, United Kingdom Manchester Metropolitan University Full time

    Project summary Rehabilitation services prove highly effective in managing numerous chronic conditions such as coronary artery disease, yet they remain underutilized among patients. Further, disparities in care are evident as the data indicates that women and individuals from socioeconomically deprived areas are notably less likely to attend rehabilitation,...


  • Manchester, United Kingdom The University of Manchester Full time

    Applications are invited for the position of Senior Lecturer in Particle Physics on the LHCb experiment. Senior Lecturer is a permanent academic staff member equivalent to associate professor in the US naming convention.We are seeking to appoint a particle physicist with an international reputation and strong-track record for leadership, research and...


  • Manchester, United Kingdom The University of Manchester Full time

    Application deadline: All year round (as long as possible) Research theme: Chemistry (Physical and Analytical Chemistry)How to apply: This studentship is funded through the Photon Science Institute at the University of Manchester, it is open to both UK and International Students and will cover full fees and a stipend at the UKRI rate (£19,237 for...


  • Manchester, United Kingdom ClearCourse Full time

    Company description: Join a rapidly growing collaborative of disruptive technology companies working together to build a brilliant software and payments business. Since our inception in 2018, we’ve acquired software and services companies at a rate of more than one a month, so as a ClearCourse employee you’ll benefit from the feel of a pioneering...


  • Manchester, United Kingdom Diversity Travel Full time

    We are a successful travel management company for the charity and academic communities and we are proud and passionate about what we do.We are currently looking for an Integrations Developer to join our expanding IT and Development team. We prioritise IT development to ensure that our technological solutions promote the industry in efficiency, security, and...


  • Manchester, United Kingdom The University of Manchester Full time

    This 3.5 year PhD project is funded by the MADSIM Project, Funding is for Home students and EU students with settled status. Funding covers home tuition fees and provides a stipend at the UKRI rate (£19,237 for 2024/25). The start date is 1st October 2024.This is an interdisciplinary project between the Department of Mathematics (Christiana Charalambous,...


  • Manchester, United Kingdom Manchester Metropolitan University Full time

    Project summaryThe impact of alopecia is highlighted in the Global Burden of Disease estimates of years lost to disability, where alopecia areata (AA) was ranked higher than both psoriasis and melanoma in disease impact.Irrespective of the underlying cause or pattern of the hair loss (diffuse thinning or patches), accurate measures of a person's hair loss...


  • Manchester, United Kingdom Manchester Metropolitan University Full time

    Project summary The impact of alopecia is highlighted in the Global Burden of Disease estimates of years lost to disability, where alopecia areata (AA) was ranked higher than both psoriasis and melanoma in disease impact. Irrespective of the underlying cause or pattern of the hair loss (diffuse thinning or patches), accurate measures of a person’s hair...


  • Manchester, United Kingdom Medivet Group Ltd Full time

    **About us** We’re a community of passionate veterinary professionals committed to providing truly exceptional care. We’re set on building something extraordinary: creating the most forward-thinking and innovative place in the veterinary industry. We’re always looking for people who aspire to stand out in their field, and it’s this vision and...

  • Solutions Architect

    6 days ago


    Manchester, United Kingdom CareerBliss Full time

    Solutions Architect (Boomi Integration)Duration: 6 MonthsStart: ASAPLocation: Manchester & remote (hybrid working)Rate: £750 per dayIR35 Status: InsideWe require a Solutions Architect with Boomi integrations experience for our higher education client who are currently running a project to transform their Integration landscape. The scope of the project is to...


  • Manchester, United Kingdom Infused Solutions Full time

    Integration Engineer contract role - NetSuite / Salesforce My client is urgently looking to hire an Integration Engineer with experience with NetSuite and Salesforce. Within the role you will be tasked with integrating NetSuite and Salesforce for the client's finances. The role will be hybrid in Cheltenham, but they will consider remote for the right...


  • Manchester, United Kingdom Time For You Full time

    Are you an experienced cleaner and looking for work in local friendly houses, where you choose the hours and days to suit you? We are looking for **self-employed **domestic cleaners to work in the South East of Manchester, you **must** live or easily be able to access the following areas: - M12 to M21. PLEASE DO NOT APPLY IF YOU LIVE OUTSIDE OF THIS AREA,...