Abstract
We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.
Highlights
The choice of an optimal numerical solver for a given fluid dynamics problem is often problematic.Memory and runtime requirements, numerical accuracy and stability, treatment of boundaries, parallel scalability and flow physics are only some of the criteria that need to be taken into consideration.In particular, many flow problems cannot be grouped into a particular solver’s “favorite problems”.One approach to locally exploit the features of different solvers consists in splitting the computational domain and apply different flow solvers on the respective subdomains.Navier–Stokes (NS) solvers [1,2] and Lattice Boltzmann (LB) methods [3,4] are well established techniques for simulating in- or weakly compressible fluid flow
One or the other method may be advantageous in particular flow scenarios, and both approaches have been compared [5,6] and studied in detail over the last decades. It is well-known that Lattice Boltzmann methods yield the Navier–Stokes equations in the asymptotics of a vanishing Mach number, and even result in the incompressibleNavier–Stokes system using diffusive scaling [7]
Schwarz methods for steady-state coupled problems may require many iterations to converge; the Anderson acceleration technique reduces the number of iterations steps. We demonstrate that these features of the Anderson acceleration hold for Lattice Boltzmann and Navier–Stokes (LBNS) coupling
Summary
The choice of an optimal numerical solver for a given fluid dynamics problem is often problematic.Memory and runtime requirements, numerical accuracy and stability, treatment of boundaries, parallel scalability and flow physics are only some of the criteria that need to be taken into consideration.In particular, many flow problems cannot be grouped into a particular solver’s “favorite problems”.One approach to locally exploit the features of different solvers consists in splitting the computational domain and apply different flow solvers on the respective subdomains.Navier–Stokes (NS) solvers [1,2] and Lattice Boltzmann (LB) methods [3,4] are well established techniques for simulating in- or weakly compressible fluid flow. One or the other method may be advantageous in particular flow scenarios, and both approaches have been compared [5,6] and studied in detail over the last decades It is well-known that Lattice Boltzmann methods yield the Navier–Stokes equations in the asymptotics of a vanishing Mach number (convective scaling), and even result in the incompressibleNavier–Stokes system using diffusive scaling [7]. When using the term “Navier–Stokes solver” in the following, we refer to a direct discretization of the (incompressible) Navier–Stokes system and a respective numerical method solving the arising non-linear system Despite their particular features—high locality (LB), local/simple treatment of complex geometries (LB), low memory requirements (NS), to only name a few—only little effort has been undertaken so far to spatially couple the two approaches [8,9,10,11,12] or, more generally speaking, to couple LB and direct PDE solvers [13,14]
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