The LS-STAG immersed boundary/cut-cell method for non-Newtonian flows in 3D extruded geometries

Abstract

The LS-STAG method is an immersed boundary/cut-cell method for viscous incompressible flows based on the staggered MAC arrangement for Cartesian grids, where the irregular boundary is sharply represented by its level-set function, results in a significant gain in computer resources (wall time, memory usage) compared to commercial body-fitted CFD codes. The 2D version of LS-STAG method is now well-established (Y.

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

“…In addition, a number of specialized methods have been designed to achieve better than first order accuracy in the L ∞ norm. These include the immersed interface (e.g., [20,21,22,23] [24,25]), ghost fluid (e.g., [26,27,28,29]), cut-cell methods (e.g., [30,31,32,33]) and Voronoi interface (e.g., [34,35]) methods. These methods modify difference stencils near the domain boundary to account for the boundary conditions.…”

Accurate discretization of diffusion in the LS-STAG cut-cell method using diamond cell techniques

“…The purpose is to assess the ability to compute accurately local heat flux at immersed boundaries, which is a sensible quantity since it involves the temperature gradient at the sold face of cut-cells. Once the DCM has been assessed on 2D flows, the DCM is applied to the Navier-Stokes equations in 3D-extruded geometries to enhance the discretization of isothermal incompressible flows computed with the LS-STAG method with 2-point discretization reported in [16]. First the spatial accuracy of the various variants of DCM is assessed on the test case of pure thermal conduction (Eq (1) with v = 0) between concentric cylinders of diameters r = R 1 and r = R 2 , where a temperature difference ∆T = T 2 − T 1 is applied.…”

“…However, the Navier-Stokes computations in [16] reported that the use of the above two-point formulas diminishes the accuracy of the LS-STAG method, and that only a superlinear order of convergence was obtained. The reason is that, when α = 0, the face-normal gradient ∂T /∂x| e cannot be written as a function of T i,j and T i+1,j only, it also has a component tangential to the face also.…”

“…The flow unsteadiness is induced by a time-varying inflow boundary condition, yielding a timeperiodic Reynolds number Re ∈ [0, 100]. This benchmark flow has previously been performed in [16] with the LS-STAG method for 3D extruded geometries, using 2-point formulas for the diffusive fluxes of the Navier-Stokes equations.…”

“…We have successfully applied the LS-STAG method to Newtonian flows at moderate Reynolds number in fixed and moving geometries [7], pseudoplastic flows [5], and viscoelastic flows [6]. In a recent paper [16], we have extended the LS-STAG discretization for 3D configurations with translational symmetry in the z direction (subsequently called 3D extruded configurations), where are only present the 4 types of cells depicted in Fig. 1(b).…”