Session F10: Computational Fluid Dynamics: Algorithms (3:55pm - 4:40pm CST)

Reconstruction of turbulent mean flow statistics in the presence of uncertainty in measurements

Measurements from experiments are usually under-resolved in space and contain partial information about the true state of the flow. Data assimilation has proven to be an effective approach to accurately reconstruct the full flow field from limited information. With the presence of strong outliers in the sparse measurements, the adjoint-based methodology with mixed-norm regularized optimization has shown to be more efficient and accurate than more common least-squares techniques. We extend our previous work on mixed-norm data-assimilation and present a robust framework using a non-linear turbulence closure model to reconstruct the time-averaged mean flow field from limited experimental measurements with associated strong outliers. The framework shows promising result for the precise recovery of the Reynolds stress, via a volumetric forcing correction in the non-linear turbulence closure model equations. Applications of this framework will be presented for the case of a turbulent separated flow at sufficiently high Reynolds number for which the point-wise sparse measurements are obtained from an actual experiment.   

A parallel-in-time approach for accelerating direct-adjoint computations

Parallel-in-time methods are commonly used to accelerate the solution of linear and nonlinear partial differential evolution equations. Among them, the PARAEXP algorithm is particularly suited for an extension to direct-adjoint system arising in computational fluid dynamics. We present a computational framework to augment the PARAEXP algorithm for the forward linear or nonlinear problem as well as the linearized backward equation. In this talk, we describe three distinct versions of the algorithm, particularly tailored to linear and nonlinear optimization problems. Gains in efficiency are seen across all cases, showing that a parallel-in-time approach is feasible for the acceleration of direct-adjoint studies. This signifies a possible approach to further increase the run-time performance for optimization studies that either cannot be parallelized in space or are at their limit of efficiency gains for a parallel-in-space approach.   

Quantum Computation of Fluid Dynamics

Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms has in some instances demonstrated, both theoretically and experimentally, higher computational efficiency than their classical counterparts. Starting with a brief introduction to quantum computing, we will distill from the huge spectrum of quantum computational methods a few key tools and algorithms, and evaluate possible approaches of Quantum Computation of Fluid Dynamics (QCFD). We will motivate this new direction by attempting to solve simple but important flow(s) such as the Stokes flow, using specific quantum-numerical integration schemes. We shall also shed some light on possible, and preliminary, ``quantum steps" towards the Navier-Stokes equation.   

A mesh refinement framework for the lattice Green's function method for incompressible flows

We develop an adaptive mesh refinement strategy compatible with the lattice Green’s function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust (conservative, stable) and computationally efficient (linear complexity) solutions. The original method is spatially adaptive, but embedded mesh refinement is challenging to integrate with the underlying LGF which is only defined for a fixed resolution. We present a strategy for mesh refinement where the solution to the pressure Poisson equation is approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. For the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is validated with numerical simulations of vortex rings. The collision of vortex rings at high Reynolds number is simulated to highlight the reduction in computational cells achievable with both spatial and the refinement adaptivity.   

Fokker-Planck Central Moment Lattice Boltzmann Method for Computation of Turbulent Flows

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by matching the changes in different discrete central moments under collision to those given by the CBE under FP collision. This can be interpreted as a new path in terms of the relaxation of the various central moments to ``equilibria'', which we term as the Markovian central moment attractors that depend on the adjacent lower order post-collision moments and the diffusion coefficient; the relaxation rates are based on scaling the drift coefficient by the order of the moment. We demonstrate its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient in accurately representing flows at high Reynolds numbers. As illustrative examples, we show 3D simulation of turbulent flows and liquid-gas systems with interfacial effects modulated by surfactant effects.   

An Unconditionally Energy-Stable Scheme for Incompressible Navier-Stokes Equations with Periodically Updated Coefficient Matrix

We present an unconditionally energy-stable scheme for simulating incompressible flows based on the generalized Positive Auxiliary Variable (gPAV) framework. The nonlinear term is reformulated into the form of a linear term plus a correction term, where the correction term is put under control by an auxiliary variable. The scheme incorporates a pressure-correction type strategy into the gPAV procedure, and it satisfies a discrete unconditional energy stability property. Upon discretization, the pressure linear system involves a constant coefficient matrix that can be pre-computed. The velocity linear system involves a coefficient matrix that is updated periodically, once every $k_0$ time steps, where $k_0$ is a user-specified integer. The auxiliary variable, being a scalar-valued number, is computed by a well-defined explicit formula, which guarantees the positivity of its computed values. The proposed method produces accurate simulation results at large or fairly large time step sizes for the incompressible Navier-Stokes equations. The impact of the periodic coefficient-matrix update on the overall cost of the method is observed to be small in typical numerical simulations. Several flow problems will be simulated to demonstrate the accuracy and performance of this method.