Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Figure 1.  Schematic of multi-PDE subdomains

Figure 2.  Abstract representation of global and local models

Figure 3.  Edge bubble function defined in the reference domain

Figure 4.  Schematic diagram of global and local models with different fidelity physics and non-matching interfacial meshes

Figure 5.  Unequal degrees of freedom between the global and local models across $ \Gamma_I $. (In the 3D case, there are 4 and 5 DOFs in the global and local meshes, respectively.)

Figure 6.  Quadrature points for the surface integral along the interface $ \Gamma_I $

Figure 7.  Geometry and boundary conditions for flow around a 2D square

Figure 8.  Non-matching mesh for flow around a 2D square

Figure 9.  Velocity and pressure fields computed on the non-matching mesh. (Green box indicates the interface.)

Figure 10.  Comparison of time-varying drag and lift coefficients for flow around a 2D square at $ Re = 250 $

Figure 11.  Velocities and pressure along the horizontal centerline. (The dotted vertical lines indicate the position of the interface.)

Figure 12.  Configuration and dimensions of the computational domain for flow over a 3D block. (The blue inner box indicates the local domain.)

Figure 13.  Matching and non-matching meshes for flow over a 3D block

Figure 14.  Vortices around a block in the fine-grid block

Figure 15.  Mean velocity magnitude computed on matching and non-matching meshes for flow over the 3D block. (The velocity magnitude is normalized by the free-stream velocity $ U_{\infty} $.)

Figure 16.  Mean pressure coefficient computed on the matching and non-matching meshes for flow over a block

Figure 17.  Mean pressure coefficient on the surface of the 3D block at $ z/d = 3 $. (The coordinate $ \xi $ represents the distance along the perimeter of the 3D block, as illstrated in the figure.)

Figure 18.  Mean streamwise velocity and velocity fluctuation along the centerline at $ z/d = $1, 3 in the wake

Figure 19.  Mean streamwise and spanwise velocities along the transverse axis at $ x/d = $2 and $ z/d = 3 $ in the wake

Figure 20.  Mean streamwise and spanwise velocity fluctuations along the transverse axis at $ x/d = $2 and $ z/d = 3 $ in the wake

Figure 21.  Energy spectrum of the streamwise velocity fluctuations along the centerline at $ z/d = $1 and $ z/d = $3 in the wake

Figure 22.  Energy spectrum of the streamwise velocity fluctuations along the transverse line at $ x/d = $2, 3.5, and $ z/d = 3 $ in the wake region

Figure 23.  Mass concentration around the 3D block in the fine-grid block over $ \Omega_L $

Figure 24.  Time-averaged mass concentration along the transverse axis at various positions, $ x/d = $1, 2, 3 in the wake region