Mathematics in paper

*Correspondence: [email protected] Centre of Computational Engineering and Integrated Design (CEID) and Department of Mathematics and Physics, Lappeenranta University of Technology, P.O. Box 20, Lappeenranta, FI-53851, Finland Abstract This paper aims to give a general overview of industrial mathematics applied to papermaking. Modelling challenges vary from computational fluid dynamics (CFD) to finite-element analyses (FEA) when the paper web transforms from a multiphase flow to a solid fibre network to a ready paper. Also, different length scales are present from fibre level to machine level problems, i.e. from millimetres up to one hundred metres. Mathematical modelling of papermaking is aiming at optimizing the process and the end-product. Thus, computational tools for optimal shape design and optimal control purposes have been developed.