A next-generation discontinuous galerkin fluid dynamics solver with application to high-resolution lung airflow simulations

Abstract

We present a novel, highly scalable and optimized solver for turbulent flows based on high-order discontinuous Galerkin discretizations of the incompressible Navier-Stokes equations aimed to minimize time-to-solution. The solver uses explicit-implicit time integration with variable step size. The central algorithmic component is the matrix-free evaluation of discretized finite element operators. The node-level performance is optimized by sum-factorization kernels for tensor-product elements with unique algorithmic choices that reduce the number of arithmetic operations, improve cache usage, and vectorize the arithmetic work across elements and faces. These ingredients are integrated into a framework scalable to the massive parallelism of supercomputers by the use of optimal-complexity linear solvers, such as mixed-precision, hybrid geometric-polynomial-algebraic multigrid solvers for the pressure Poisson problem. The application problem under consideration are fluid dynamical simulations of the human respiratory system under mechanical ventilation conditions, using unstructured/structured

Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations

“…In this publication, we focused on geometrically refined meshes consisting only of hexahedral shaped cells, where all cells have the same polynomial degree p. However, the presented algorithms work both for p-and for hp-adaptive problems, where the polynomial degree varies for each cell, as well as for simplex or mixed meshes, as the implementation in deal.II [24] shows. Moreover, they are-as demonstrated in [17]-applicable also for auxiliary-space approximation for DG. acknowledged for generous allotment of compute time on Palmetto cluster.…”

“…It relies on auxiliary-space approximation [16], i.e., the transfer into a continuous space, as well as on sequential execution of p-multigrid, h-multigrid, and AMG. In [17], that solver was extended to leverage locally refined meshes. In [18][19][20][21], matrixfree implementations of parallel geometric local-smoothing algorithms for CPU and GPU were investigated and comparisons with AMG were conducted.…”

“…The algorithms presented in this publication have been integrated into the open-source finite-element library deal.II [23] and are mostly part of its 9.3 release [24]. Their implementation has been used in [17] to simulate the flow through a lung geometry and is applied in the ExaDG incompressible Navier-Stokes solver [3]. All results of this publication have been obtained with small benchmark programs leveraging on the infrastructure of deal.II.…”

“…The results obtained in this publication for continuous FEM are transferable to the DG case, where one does not have to consider hanging-node constraints but fluxes between differently refined cells. In the case of auxiliary-space approximation [17], this difference only involves the finest level and the rest of the multigrid algorithm could be as described in this publication.…”

From anomalous dissipation through Euler singularities to stabilized finite element methods for turbulent flows

“…While computationally fast solvers based on H 1 -conforming methods often rely on projection methods (see e.g. [113][114][115]), these implementations use filtering or spectral-vanishing viscosity methods to realize dissipative mechanisms. This circumstance might indicate the need for further research in the direction of stabilized H 1 -conforming methods with projection-type time integration, or point to an advantage of non-conforming methods in this regard.…”