Position:Shell – University of Adelaide scholarship
Location: School of Chemical Engineering, University of Adelaide
Duration: 3–5 years
Closing date: 31 August 2024
About
Stable Unique Riemann Solution For 2×2 Hyperbolic System
Multiple discontinuous solutions of conservation law systems is a well-known phenomenon. Selection of unique solution has been performed by either stability criteria or asymptotic vanishing dissipation method. Recently developed splitting mapping and the asymptotic method of matched singular first-order expansions allow deriving unique solutions of several Riemann problems. One of those relates to in situ storage of CO2 and hydrogen in geological formations, which is a top priority in Australian energy sector.
The scope comprises derivation of unique Riemann solution for 2×2 hyperbolic system stable with respect to vanishing diffusion and capillary pressure. The topological aspect included description of the phenomenon in terms of classification of singular points of smooth manifolds. The industrial application includes using the Riemann solution in 3D commercial stream-line reservoir simulator.
To Apply
Please contact Pavel Bedrikovetski
- Bedrikovetsky, P., 2013. Mathematical theory of oil and gas recovery. Springer Science & Business Media. 600p.
- Borazjani, S., Roberts, A.J. and Bedrikovetsky, P., 2016. Splitting in systems of PDEs for two-phase multicomponent flow in porous media. Applied Mathematics Letters, 53, pp. 25–32.
- Borazjani, S. and Bedrikovetsky, P., 2017. Exact solutions for two-phase colloidal-suspension transport in porous media. Applied mathematical modelling, 44, pp. 296–320.
- Nazaikinskii, V.E., Bedrikovetsky, P.G., Kuzmina, L.I. and Osipov, Y.V., 2020. Exact Solution for Deep Bed Filtration with Finite Blocking Time. SIAM Journal on Applied Mathematics, 80(5), pp. 2120–2143.
- Russell, T. and Bedrikovetsky, P., 2024. Exact solution for water evaporation during CO2 injection. Water Resources Research, 60(6), p.e2023WR036600.
