TY - JOUR
T1 - An Accurate and Scalable Direction-Splitting Solver for Flows Laden with Non-Spherical Rigid Bodies – Part 1: Fixed Rigid Bodies
AU - Goyal , Aashish
AU - Wachs , Anthony
JO - Communications in Computational Physics
VL - 4
SP - 1079
EP - 1132
PY - 2023
DA - 2023/11
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0176
UR - https://global-sci.org/intro/article_detail/cicp/22131.html
KW - Highly scalable solver, particle-laden flow, particle resolved direct numerical simulation, incompressible flow, non-spherical rigid bodies.
AB - <p style="text-align: justify;">Particle-resolved direct numerical flow solvers predominantly use a projection method to decouple the non-linear mass and momentum conservation equations.
The computing performance of such solvers often decays beyond $\mathcal{O}(1000)$ cores due to
the cost of solving at least one large three-dimensional pressure Poisson problem per
time step. The parallelization may perform moderately well only or even poorly sometimes despite using an efficient algebraic multigrid preconditioner [38]. We present an
accurate and scalable solver using a direction splitting algorithm [12] to transform all
three-dimensional parabolic/elliptic problems (and in particular the elliptic pressure
Poisson problem) into a sequence of three one-dimensional parabolic sub-problems,
thus improving its scalability up to multiple thousands of cores. We employ this algorithm to solve mass and momentum conservation equations in flows laden with fixed
non-spherical rigid bodies. We consider the presence of rigid bodies on the (uniform
or non-uniform) fixed Cartesian fluid grid by modifying the diffusion and divergence
stencils on the impacted grid node near the rigid body boundary. Compared to [12],
we use a higher-order interpolation scheme for the velocity field to maintain a second-order stress estimation on the particle boundary, resulting in more accurate dimensionless coefficients such as drag $C_d$ and lift $C_l.$ We also correct the interpolation scheme
due to the presence of any nearby particle to maintain an acceptable accuracy, making
the solver robust even when particles are densely packed in a sub-region of the computational domain. We present classical validation tests involving a single or multiple
(up to $\mathcal{O}(1000))$ rigid bodies and assess the robustness, accuracy and computing speed
of the solver. We further show that the Direction Splitting solver is ∼5 times faster on
5120 cores than our solver [38] based on a classical projection method [5].</p>