Adaptive Stabilized Galerkin Methods with Multiphysics Applications

Objective:

Advanced computer-aided simulation methods are of vital importance for solving many engineering applications. This project focuses on the development of Adaptive Stabilized Galerkin Methods and their application to a number of challenging engineering multiphysics problems. The main objective is to develop a three-dimensional simulation framework that will incorporate the use of stabilized formulations, grid-adaptivity, and higher order methods. These three features enable to tackle challenging engineering applications that cannot be solved otherwise. The software implementation will execute on large parallel machines as well as in multi-core workstations and it will employ already existing libraries such as PETSc (solvers of linear equations). The research group has ample experience on the development of methods and large simulation software packages. Specifically, David Pardo (PI) has been working for over ten years in the development of two- and three-dimensional hp-adaptive finite element methods, Dr. Johan Jansson (co-PI) has been involved with the FEniCS project (automated solution of PDE by FEM) for 9 years with adaptive error control, HPC and advanced multi-physics methods and applications, and Dr. Lakhdar Remaki has also worked on the development of large finite volume simulators for the industry and advanced applications. The remaining members of the team have also developed or worked on finite element methods and/or software for solving partial differential equations. Using the three-dimensional simulation framework, four engineering applications will be studied during this project: (a) multiphysics forward and inverse problems in petroleum engineering, (b) optimal design of turbofans, (c) gas particle multiphysics simulations, and (d) turbulent fluid-structure interaction. Various members of the team have worked with industry partners in each of the above four application areas. As a result of this project, we will: (1) publish over 20 scientific articles in ISI journals with high impact factor and deliver over 20 presentations at international workshops, (2) develop an 'in house' simulation framework that uses the most advanced adaptive and stabilization methods, (3) demonstrate the practical use of the software by applying it to various challenging multiphysics applications, and (4) train new researchers in the area of computational and applied mathematics.