This book is concerned with the study of methods in high-performance computing (HPC) for simulation and optimisation of flow problems that typically occur in the framework of microflows. We consider the adequate use of techniques in parallel computing by means of finite element based solvers for partial differential equations (PDEs) and by means of sensitivity- and adjoint-based optimisation methods. The main focus is on low Reynolds number flow describing the distribution of species concentration within the fluid. Conclusively, we aim to optimise such a microfluidic system by applying an electric potential difference to influence the mixing of the species using electrokinetic properties of the fluid.