Imanol García de Beristain will defend his doctoral thesis on March 9th

Imanol García de Beristain joined BCAM-Basque Center of Applied Mathematics as an Internship within the CFD Modelling and Simulation in 2012, coming from the University of the Basque Country, Spain (UPV/EHU Euskal Herriko Unibertsitatea - Universidad del País Vasco, Spain) where he obtained his BA diploma on Chemical Engineering at the same year in which he also graduated in MSc Process Systems Engineering tin a double degree program at Cranfield University (UK). He did a second MSc in "Research in Mathematics" before he started his PhD on the CFD field.

His PhD thesis has been directed by Lakhdar Remaki, Alfaisal University, Saudi Arabia and External Scientific Member of BCAM and Luis Vega, Scientific Director of BCAM.

The defense will take place onMarch 9, 2018, 12:00h, P1A1 Aula de Grados, Escuela de Ingenieros de Bilbao (UPV/EHU), Basque Country, Spain.

Title: On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation.

Abstract:

In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme is developed as a means to reduce the computational cost associated with aeroacoustic simulations, which are unsteady in nature with high-order requirements for the acoustic wave propagation. We start by constructing a set of governing equations for the hybrid computational aeroacoustics method, splitting the problem into two steps: acoustic source computation and wave propagation.

The first step solves the incompressible Navier-Stokes equation using Chorin’s projection method, which can be understood as a prediction-correction method. First, the velocity prediction is obtained solving the viscous Burgers’ equation. Then, its divergence-free correction is performed using a pressure Poisson type projection. In the velocity prediction substep, Burgers’ equation is solved using two ABS variants: a MAC type implementation, and a “modern” ADER method. The second step in the hybrid method, related to wave propagation, is solved combining ABS with the discontinuous Galerkin high-order approach. Described solvers are validated against several test cases: vortex shedding and Taylor-Green vortex problems for the first step, and a Gaussian wave propagation in the second case.

Although ABS is a multiderivative type scheme, it is easily programmed with an elegant recursive formulation, even for the general Navier-Stokes equations. Results show that its simplicity combined with excellent adaptivity capabilities allows for a successful extension to very high-order accuracy at relatively low cost, obtaining considerable time savings in all test cases considered.