Design, derivation, and implementation of mesh-free finite volume solvers based on 3D unit cell morphology to estimate biomass particle effective parameters

Overview

The aim of this PhD project is to use lignocellulosic morphological features extracted from high resolution micro-CT images of biomass particles undergoing a dilute acid pretreatment process to perform computational homogenisation over representative unit cell configurations. Mesh-free finite volume solvers will be developed based on 3D point cloud data sets to estimate virtual biomass particle effective parameters, such as diffusivity, thermal conductivity, and permeability. The simulation results will be analysed to provide a fundamental understanding of the impact that changes in pore structure and composition have on the effective parameters as the particle undergoes enzymatic hydrolysis.

This work forms part of the supervisory team's ARC Discovery Project DP230102299 Transforming Australian bio-based industries through multiscale modelling.

Research activities

This project involves the development of partition of unity, radial basis function techniques implemented in a mesh-free framework to solve local unit cell problems, defined over irregularly shaped domains, that are expressed in terms of partial differential equations subjected to periodic boundary conditions on the external boundaries and appropriate continuity conditions at internal interfaces between the solid and void space. This strategy leads to a regularised least squares method for solving these problems over the virtual biomass particle morphology. Regularisation will be used to make the penalised least squares system relatively well-conditioned. Efficient solution methods will be investigated to solve the large system that approximately enforces the external boundary and interface conditions. The entries in the effective parameter tensors are then obtained by integrating over the unit cell using an appropriately chosen quadrature rule.

Outcomes

• New numerical algorithms for computational homogenisation.
• Novel imaged-based modelling techniques for virtual biomass particles.
• High impact publications in the applied and computational mathematics literature.

Skills and experience

The student should have:

• strong programming skills (e.g. MATLAB, Julia or equivalent)
• completed undergraduate units in numerical linear algebra and computational mathematics (e.g. MXB326) and partial differential equations (e.g. MXB322).

Scholarships

You may be eligible to apply for a research scholarship.

Explore our research scholarships

Keywords

• applied mathematics
• computational mathematics
• image analysis
• partial differential equations

Contact

Contact the supervisor for more information.