Numerical simulation of two-dimensional and three-dimensional axisymmetric advection–diffusion systems with complex geometries using finite-volume methods

Abstract

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection-diffusion systems. The motivation behind this is threefold. Firstly, the ability to model the correct geometry of a situation yields more accurate results. Secondly, smooth geometries eliminate corner singularities in the calculation of, for example, mechanical variables and thirdly, different geometries can be tested for experimental applications. An example illustrating each of these is given: fluid carrying a dye and rotating in an annulus, bone fracture healing in mice, and using vessels of different geometry in an ultracentrifuge.

Computational model-informed design and bioprinting of cell-patterned constructs for bone tissue engineering

“…The ROWMAP solver used to solve the system of partial differential equations requires that the geometrical domain is subdivided into rectangular subdomains, meaning that the domain boundary will be composed of straight lines. As the computational time scales with the number of rectangles, we have previously established a simplified domain geometry that coarsens the smooth outer surface of the periosteal callus into discrete steps, without a loss of accuracy in predicted bone healing outcomes [44]. To simulate the bone regeneration process in a large segmental bone defect, a gap size of 4 mm was used, which is in the same range as other mouse femoral critical defect sizes reported in the literature: 2 mm [45], 3 mm [46], 3.5 mm [47], 4 and 5 mm [43].…”

Exploring the phase explosion of water using SOM-mediated micro-bubbles

“…This 2D treatment suffices under the assumption that the dynamics is symmetric around the z-axis. 23 The advection-diffusion partial differential equation when expressed in 2D Cartesian co-ordinates is…”