Abstract

Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures 1) the Control Volume Function Approximation (CVFA), and 2) the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate.

Abstract

The present work investigates the efficiency of the Multigrid method when applied to solve two-dimensional laminar steady free convection flow in a square enclosure with a partially heated from below. The numerical method includes finite volume discretization with upwind scheme on structure orthogonal regular meshes. Performance of the correction storage (CS) Multigrid algorithm is compared for different numbers of sweeps in each grid level. Up to four grids, for both Multigrid V- and W- cycles, are presented. The results are mainly analyzed in terms of the average heat transfer at the walls of the enclosure and Multigrid performance on the rate of convergence. It is also shown that convective heat transfer has a characteristic behavior for each boundary conditions adopted in given ranges of the governing parameters.

Abstract

time integration. We are motivated by three-dimensional unsteady compressible flow applications, which often result in large stiff systems. Implicit time integrators overcome the impact upon restrictive CFL conditions on explicit ones but leave the problem to solve huge nonlinear systems. In this paper we consider a multigrid preconditioning strategy for Jacobian-free Newton-Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretizations. The preconditioner is defined by an auxiliary first order Finite Volume (FV) discretization that refines the original DG mesh, but can still be implemented algebraically. Different options exist to define the grid transfer between DG and FV. We suggest an ad hoc assignment of the unknowns as well as L₂ projections. We present new numerical results for the two-dimensional convection-diffusion equation in combination with the different transfer options, which demonstrate the quality and efficiency of the suggested preconditioner with regards to convergence speed up and CPU time. The suggested L₂ projection from this paper result in the best convergence speed up.

Abstract

A relaxed, high-order, Multidimensional Optimal Order Detection (MOOD) framework is extended to the simulation of compressible multicomponent flows on unstructured meshes in the open-source unstructured compressible flow solver UCNS3D. The class of diffuse interface methods (DIM) is employed with a five-equation model. The high-order CWENO spatial discretisation is selected due to its low computational cost and improved non-oscillatory behaviour compared to the original WENO variants. The relaxed MOOD enhancement of the CWENO method has been necessary to further improve the robustness of the CWENO method. A series of challenging compressible multicomponent flow problems have been implemented in UCNS3D, including shock wave interaction with a water droplet and shock-induced collapse of bubbles arrays. Such problems are generally very stiff due to the strong gradients present, and it has been possible to tackle them using the extended MOOD-CWENO numerical framework.

Abstract

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.