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Novel techniques for modelling with partial differential equations in heterogeneous media

Mathematical models involving heterogenous media comprising two or more constituent materials with different physical properties are widespread across scientific and engineering disciplines.For example, modelling the flow of pollutants or water below the earth’s surface involves dealing with a highly heterogeneous geological structure.Solving such mathematical models is particularly challenging when the heterogeneity is explicitly accounted for in the model.As a result this project aims to answer natural questions such as:Can we develop accurate and efficient numerical or semi-analytical methods to solve …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Modelling and simulation of heterogeneities

We are offering opportunities to conduct research in developing computationally efficient, dual scale modelling approaches for simulating multiphase transport in heterogeneous porous media by computing entirely over a microcell (unit cell) derived directly from images of the morphology of the porous medium.This has importance to such disparate applications as ground water flow, the extraction of coal seam gas and the electrophysiology of a heterogeneous heart. There are additional complexities in terms of developing and implementing new numerical approaches that may …

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Multiscale computational modelling of heterogeneous transport processes

Computational models of a multiscale nature, whether they involve partial differential equations with fine-scale variation in coefficients or distinct processes at multiple scales, are ubiquitous across engineering and scientific disciplines. For such problems, direct numerical solution of the governing equations is infeasible due to the huge amount of computational resources required to resolve the smaller scale.Such numerical issues motivate the need for either spatial-averaged models that aim to efficiently and accurately approximate the averaged fine-scale solution on a coarser scale …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Development of 3D-printed heterogeneous catalyst for biomass processing

The current methods for the manufacture of structured catalysts are complex and expensive; simple methods to deposit a desired geometry of catalysts into engineered channels are crucial to cost reduction. The aim of this project is to develop new catalytic conversion technologies to hydrotreat bio-crudes derived from biomass.

Study level
PhD, Master of Philosophy
Faculty
Science and Engineering Faculty
Lead unit
School of Chemistry, Physics and Mechanical Engineering

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