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[CT103]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We present a methodology for finite volume discretizations using “embedded boundaries” in applications with complex geometries and moving interfaces, while avoiding complex boundary-fitted meshes. We demonstrate 4th-order and higher accuracy for physical jump conditions; numerical stability, even with extremely small volumes; and adaptive mesh refinement. Using parallel HPC with GPU acceleration, we achieve fast, high-resolution simulations across applications in fluid dynamics, heat transfer, and a variety of nonlinear PDEs.
Classification : 65M08, 35Q35, 65Y05
Author(s) :
- Hans Johansen (Lawrence Berkeley Laboratory)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We consider the piston problem of gas dynamics, described by the Lagrangian formulation of the Euler equations for an ideal compressible gas. While a highly accurate numerical solution can be obtained in the interior of the domain through state-of-the-art techniques like WENO reconstruction and SSP-RK time-stepping, boundary discretization can lead to unphysical reflections. We investigate and implement several efficient boundary conditions to deal with this problem without significantly increasing the size of the computational domain.
Classification : 65M08, 65M22, 76N30, 35L04, 35L65
Author(s) :
- Carlos Muñoz (KAUST)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We derive the mathematical model that allows chemotaxis in avascular tumour growth in a two-phase medium. The two phases are the viscous cell phase and the inviscid fluid phase. The conservation of mass-momentum is incorporated in each phase, and appropriate constitutive laws are applied to formulate the governing equations. Further, these equations are simplified into three main variables : cell volume fraction, cell velocity, and nutrient concentration. These variables generate a coupled system of non-linear partial differential equations. A numerical scheme based on the finite volume method is applied to approximate the solution of cell volume fraction. The finite element method is applied to approximate the solutions of cell velocity and nutrient concentration. We investigate tumour growth when when tumour cells move along a fluid containing a diffusible nutrient to which the cells are drawn. We perform some numerical simulations to show the effect of the parameters. The findings of this literature are compatible with the existing literature.
Classification : 65M08, 92C17, 65M60
Author(s) :
- Paramjeet Singh (Thapar Institute of Engineering & Technology, Patiala)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk we study numerical approximations to the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods. Several questions are considered: the influence of including snapshots that approach the velocity time derivative and the influence of considering different discretizations for the nonlinear term in the full order model and the reduced order model. Error bounds with constants independent of the Reynolds numbers are obtained in the numerical analysis.
Classification : 65M12, 65M15, 65M60
Author(s) :
- Julia Novo (Universidad Autónoma de Madrid)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We present some recent advances on proper orthogonal decomposition (POD) methods for the Navier-Stokes equations. Among them, recovering the pressure in a robust manner when the snapshots are discretely divergence-free. We analyze the different sources of error and how they affect the pressure recovery. We also study how to adapt the POD method for varying values of the Reynolds number.
Classification : 65M12, 65M15, 65M60
Author(s) :
- Bosco García-Archilla (Universidad de Sevilla)