This book results from the XVIII Spanish-French School 'Jacques Louis Lions' on Numerical Simulation in Physics and Engineering, that took place in Las Palmas de Gran Canaria from 25th to 29th June 2018. These conferences are held biennially since 1984 and sponsored by the Spanish Society of Applied Mathematics (SEMA). They also have the sponsorship of the Société de Mathématiques Appliquées et Industrielles (SMAI) of France since 2008. Each edition is organized around several main courses and talks delivered by renowned French/Spanish scientists. This volume is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.

Destuynder, P. and Fabre, C.,  An introduction to quasi-static aeroelasticity.- Burés, M. et al., Computational treatment of interface dynamics via phase-field modeling.- Gallouët, T. et al., Consistent internal energy based schemes for the compressible Euler equation.- Chen, Y. et al., Comparison and analysis of natural laminar flow airfoil shape optimization results at transonic regime with bumps and trailing edge devices solved by Pareto games and EAs.- Ait Ameur, K. et al., Time-parallel algorithm for two phase flows simulation.- Escalante, C. et al., Modelling of bedload sediment transport for weak and strong regimes