The accurate approximation of the surface tension force is paramount for continuum surface models in the field of computational fluid dynamics for multiphase flow where surface tension is relevant. This involves being able to accurately calculate the curvature at the interface. This study focuses on the use of convolution in smoothing the VOF colour field in order to obtain better approximations of the curvature. Given the sudden jump in values of the VOF colour field, the calculation of its derivative for the curvature is sensitive to errors, given the large values of high order terms that determine the truncation error. To deal with this problem, convolution of this abruptly varying field can be used to create a smoother transition. The curvature approximation of a circular interface improved as the support of the convolution was increased.
It was proven analytically that, for these interfaces, the original curvature is retrieved from the convoluted field. Interfaces along which the curvature varies were also considered, and it was found that there is a critical convolution support that minimizes the error in the curvature, given that the choice of the support length can modify the curvature that is estimated.
An algorithm was implemented in OpenFOAM that calculates the convolution of the VOF colour field. The resulting smoothed field was then used to calculate the curvature, which is needed for the surface tension force of the system. The simulations of a two-dimensional rising bubble resulted in more accurate results for the circularity and the rising velocity, when compared to the original OpenFOAM implementation with no smoothing. With the convolution algorithm, the terminal velocity deviated only 0.01% from a well-accepted benchmark case, a great improvement when compared to the 4.2% difference when no smoothing was used. However, simulations of a static bubble in zero-gravity rapidly resulted in unphysical flow, manifested as a wavy interface, when a convolution support larger than 2 cells was chosen. An improvement of the estimation of the surface tension force direction may be needed for this behaviour to disappear.

We have explored the concept of mobile computational fluid dynamics (CFD) solving. Using the computational
power of a smartphone we tried to generate real time simulations of relatively simple transient natural
convection problems in the laminar regime. The focus lies on finding a compromise between accuracy, speed
and stability: we want to make a real timemobile CFD solver that is as accurate as possible.
A JAVA application has been created that runs on Android. The SIMPLE algorithm has been implemented
in order to solve for the flow and heat transfer. The SIMPLE algorithm on the application was tested for
runtime performance and accuracy.
For a test problem, a real time simulation on a Nexus 5X has been realized with an accuracy of 5.4% on a
21x21 grid. Running the algorithm on a desktop gave a simulation 10 times faster than real time. Comparing
this algorithm to a version converted to MATLAB, gave similar solving speed. We concluded that the bottleneck
in the algorithm, solving matrix equations, could not be easily improved, because MATLAB solvers
perform quite optimal: a significantly faster CFD solver implementing the SIMPLE algorithm probably does
not exist.
Nevertheless, when trying to use the obtained results on water and air, we could not obtain any real time
solutions. It is up to further research to define restictions that can guarantee real time solutions for fluids.