Isogeometric analysis for turbulent flow

Abstract

The article is devoted to the simulation of viscous incompressible turbulent fluid flow based on solving the Reynolds averaged Navier-Stokes (RANS) equations with different k − ω models. The isogeometrical approach is used for the discretization based on the Galerkin method. Primary goal of using isogeometric analysis is to be always geometrically exact, independent of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization SUPG technique in equations for k and ω. The solutions are compared with the standard benchmark example of turbulent flow over a backward facing step.

Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations

“…The conjugate gradient iterative solver from PETSc [2] , preconditioned by the incomplete Cholesky decomposition was used for solving the linear system. The absolute precision for preconditioned residuals was set to 10 −18 , so that "exact" solutions were obtained.…”

“…It can be described by (7) with the following choice of the potential: V (r) ≡ − 1 Fig. 9 depicts the convergence of the charge density ρ to a reference value: (ρ − ρ ref ) 2 is shown.…”

“…[45] . It has an interface to many external solvers and preconditioners, for example the UMFPACK sparse direct solver [18] , PETSc iterative solvers and preconditioners [2] , or pysparse eigenvalue solvers [24] . SfePy also supports distributed memory parallel computing with MPI using PETSc parallel vectors, matrices, and solvers as interfaced by the petsc4py package [17] .…”

“…In principle, IGA is a modification of FEM which employs shape functions with a higher order of continuity, such as B-splines, NURBS [42] , T-splines [4] , etc. It was successfully employed for numerical solutions of various physical and mathematical problems, such as fluid dynamics [3] , diffusion and other problems of continuum mechanics [14,16,31,32] . The first application of IGA in electronic structure calculations has been published in [35] .…”

Numerical Simulation of Lid-Driven Cavity Flow by Isogeometric Analysis

“…Because of many advantages of the IgA, the method has been successfully applied in various practical problems, like linear elasticity, structural vibrations, phase transition phenomena, fluid flow simulation, plate and shell analysis, heat transfer analysis, shape optimization, etc., see e.g. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”