Tony Saad

University of Utah | UOU · Department of Chemical Engineering

We derive high-order estimates of the instantaneous pressure for projection-type solvers of the incompressible Navier-Stokes equations. Projection methods play a central role in incompressible and low-Mach fluid flow simulations. However, these methods are known to produce a first-order instantaneous pressure at the end of a timestep, even when use...

Unmanned Aerial Vehicles (UAVs) are a popular platform for air quality measurements. For vertical measurements, rotary-wing UAVs are particularly well-suited. However, an important concern with rotary-wing UAVs is how the rotor-downwash affects measurement accuracy. Measurements from a recent field campaign showed notable discrepancies between data...

This note addresses the question of whether stage pseudo-pressures can be used to build high-accuracy instantaneous pressure estimates in the context of projection-based Navier-Stokes solvers. The construction of such estimates using inter-stage pseudo-pressures is not straightforward, especially when time-dependent boundary conditions are present....

We derive three-dimensional stable timestep formulas for high-order explicit time integration of the advection–diffusion equation. The proposed formulas cover explicit first, second, third, and fourth-order Runge–Kutta integrators in time as well as upwind, central, second-order, high-order upwind (k-schemes), and flux-limiters for the advection te...

The Buckingham Pi (Π) theorem is useful in determining the dimensionless terms that describe a physical phenomenon. The number of these terms grows with the number of variables. The traditional approach in identifying dimensionless quantities for a given system can be tedious and error-prone. BuckinghamPy is a Python software that automates the tra...

We derive a novel class of low-cost explicit Runge-Kutta (RK) methods for the incompressible Navier-Stokes equations using pressure-based methods. Pressure-based methods require the solution of a Poisson equation for the pressure which is subsequently used to enforce mass conservation. In most cases, the Poisson equation is an expensive proposition...

The COVID-19 pandemic forced performing arts groups to cancel shows and entire seasons due to safety concerns for the audience and performers. It is unclear to what extent aerosols generated by wind instruments contribute to exposure because their fate is dependent on the airflow onstage. We use transient, second-order accurate computational fluid...

The use of low-cost air pollution sensors mounted on drones is an exciting new approach to conduct affordable and highly resolved air quality measurements. However, the air flow around a drone consists of complex, unsteady turbulent structures which interact directly with ambient particulate matter and gases. These interactions influence the transp...

The modified equation is a useful tool in the analysis of numerical methods for partial differential equations (PDEs). It gives insight into the stability, diffusion, and dispersion properties of a given numerical scheme. Its derivation, however, is rather tedious and error-prone due to the enormous amount of algebra involved. PyModPDE is a python...

The Uintah computational framework is used for the parallel solution of partial differential equations on adaptive mesh refinement grids using modern supercomputers. Uintah is structured with an application layer and a separate runtime system. Uintah is based on a distributed directed acyclic graph of computational tasks, with a task scheduler that...

PyMaxEnt is a software that implements the principle of maximum entropy to reconstruct functional distributions given a finite number of known moments. The software supports both continuous and discrete reconstructions, and is very easy to use through a single function call. In this article, we set out to verify and validate the software against se...

These are the slides associated with our paper "A Framework for Analyzing the Temporal Accuracy of Pressure Projection Methods" (dx.doi.org/10.2514/6.2019-3634) or @ research gate: https://www.researchgate.net/publication/333807365_A_Framework_for_Analyzing_the_Temporal_Accuracy_of_Pressure_Projection_Methods

If you work in computational fluid dynamics, then you are probably aware of the Taylor-Green vortex-at least the two-dimensional case. A simple google search will land you on this wikipedia page. The classic solution there is presented in the form u = cos x sin yF(t); v = − sin x cos yF(t); F(t) = e −2νt (1) There are also many variants on this for...

Jupyter Notebook here: https://git.io/fjRjL] For an explicit compressible algorithm the maximum timestep one can take is dictated by both the advective and acoustic speeds in the flow. This is given by the famous CFL condition V δt ∆x ≤ 1 (1) where V is the maximum speed in the flow. In this case, V = u + c (2) where u is the advective speed and c...

You're probably using the Taylor vortex in the wrong way.

The Taylor vortex is a classic analytical solution of the Navier-Stokes equations that is heavily used in the CFD community as a verification tool. In its most useful form, it is given by 1 u(x, y, t) = u f-Aβ cos[α(x − u f t)] sin[β(y-f t)]e −(α 2 +β 2)νt (1) (x, y, t) = f + Aα sin[α(x − u f t)] cos[β(y-f t)]e −(α 2 +β 2)νt (2) One can easily veri...

Kelvin’s minimum energy theorem predicts that the irrotational motion of a homogeneously incompressible fluid in a simply connected region will carry less kinetic energy than any other profile that shares the same normal velocity conditions on the domain’s boundary. In this work, Kelvin’s analysis is extended to regions with boundaries on which the...

The mean gaseous motion in solid rocket motors has been traditionally described using an inviscid solution in a porous tube of fixed radius and uniform wall injection. This model, usually referred to as the Taylor–Culick profile, consists of a rotational solution that captures the bulk gaseous motion in a frictionless rocket chamber. In practice, h...

This comment aims at addressing a mass conservation issue in a paper published in the physics of fluids. The paper [R. H. Kraichnan, “Diffusion by a random velocity field,” Phys. Fluids 13(1), 22 (1970)] introduces a novel method to generate synthetic isotropic turbulence for computational purposes. The method has been used in the literature to gen...

To address the coding and software challenges of modern hybrid architectures, we propose an approach to multiphysics code development for high-performance computing. This approach is based on using a Domain Specific Language (DSL) in tandem with a directed acyclic graph (DAG) representation of the problem to be solved that allows runtime algorithm...

The Uintah computational framework is used for the parallel solution of partial differential equations on adaptive mesh refinement grids using modern supercomputers. Uintah is structured with an application layer and a separate runtime system. The Uintah runtime system is based on a distributed directed acyclic graph (DAG) of computational tasks, w...

We develop a novel transformation that maps the linear, non-homogeneous, multidimensional population balance equation (PBE) into an advection equation that is readily solved using the method of characteristics. The PBEs targeted by this transformation exclude aggregation and breakage. In addition, internal coordinates are assumed to grow independen...

This study presents the results of computational fluid dynamics (CFD) simulations of a multiphase, reacting, turbulent mixing layer in an idealized geometry. The purpose is to compare Large-Eddy Simulation (LES) to One-Dimensional Turbulence (ODT) and examine the trends of the flow under differing mixing conditions. Aqueous streams are mixed togeth...

The Uintah Software framework was developed to provide an envi-ronment for solving fluid-structure interaction problems on struc-tured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids together with a novel asynchronous task-based approach with...

Verification and validation of reconstructed neutron flux based on the maximum entropy method is presented in this paper. The verification is carried out by comparing the neutron flux spectrum from the maximum entropy method with Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta (Attila). A spherical 100% 235U critical assembly is...

A new explicit variable-density pressure projection method is proposed with a focus on transient low- Mach-number reacting flows. Our approach is based on solving the pressure Poisson equation and is suitable for implementation in fully-explicit codes. The method thus requires less computational eort compared to existing variable-density projection...

The Navier–Stokes formulation represents a uniquely challenging system of partial differential equations that continues to influence modern applied science and engineering. In its simplest form, the system can be used to prescribe the motion of a viscous incompressible fluid with constant properties. It consists of four equations in three-dimension...

We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flo...

The compressible motion of gases has long been connected with high energy yield devices such as combustors, jet engines, turbines, and rocket motors. Most available formulations for this high speed gaseous environment lead to coupled nonlinear PDEs. While their integration requires the use of numerical methods, their stability and convergence remai...

The mean gaseous motion in solid and, less commonly, hybrid rocket motors has been traditionally described assuming inviscid flow in a porous cylinder of fixed radius and constant mass addition at the sidewall. This model, usually referred to as the Taylor-Culick profile, is a simple inviscid rotational solution that captures the bulk gaseous motio...

The design of robust computational physics codes has always been a challenge to application programmers. One of the key diffculties in writing multiphysics codes stems from the inefficient handling of spatial discretization and field operations. For example, in the context of the finite volume (FV) method, one often deals with structured and unstru...

We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flo...

Kelvin's minimum energy theorem predicts that the irrotational motion of a homogenously incompressible fluid in a simply connected region will carry less kinetic energy than any other profile that shares the same normal velocity conditions on the domain's boundary. In this work, Kelvin's analysis is extended to regions with open boundaries on which...

The Navier-Stokes formulation represents a uniquely challenging system of partial differential equations that continues to influence modern applied science and engineering. In its simplest form, the system can be used to prescribe the motion of a viscous incompressible fluid with constant properties. It consists of four equations in three-dimension...

The Taylor—Culick solution for a porous cylinder is often used to describe the bulk gas motion in idealized representations of solid rocket motors. However, other approximate solutions may be found that satisfy the same fundamental constraints. In this vein, steeper or smoother profiles may be observed in either experimental or numerical tests, par...

In a previous article, an energy optimization technique was used to derive multiple solutions for the bidirectional vortex. These were obtained for a single mantle describing a single flow reversal scenario. However, the existence of multiple mantles sustaining compound flow turns has been reported in previous work. The current study focuses on the...

In this paper, Taylor's incompressible and rotational flow in a porous channel with surface mass addition is extended to account for arbitrary headwall injection. Our analysis considers Euler's steady-state equations from which an approximate solution is derived. The resulting mean flow representation satisfies the vanishing axial velocity conditio...

In this paper we present the performance analysis of a parallel Algebraic Multigrid Solver (AMG) for a finite volume unstructured CFD code. The multigrid solver is part of an unstructured cell-centered finite volume code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm....

In this study, two families of solutions are developed for the bidirectional vortex in a cylindrical chamber using Lagrangian optimization. Our optimization procedure is applied to the kinetic energy of the system and is prompted by the idea that a fluid will follow the path of least kinetic energy in the absence of forcing. Once the solution with...

This article deals with the implementation and performance analysis of a parallel algebraic multigrid solver (pAMG) for a finite-volume, unstructured computational fluid dynamics (CFD) code. The parallelization of the solver is based on the domain decomposition approach using the single program, multiple data paradigm. The Message Passing Interface...

Taylor's incompressible and rotational profile is extended to a porous cylinder with arbitrary headwall injection. This profile, often referred to as Culick's mean flow, is now generalized to permit the imposition of reactive headwall conditions. Starting with Euler's steady equations, the solution that we derive is approximate, being exact only at...

The Taylor-Culick solution for a porous cylinder has long been used to describe the bulk gas motion in idealized representations of solid rocket motors. By superimposing an arbitrary headwall injection velocity, a modified form of this solution can be extended to hybrid rocket applications and to solids with reactive headwall. However, the Taylor-C...

In a recent study, Taylor's incompressible and rotational core flow in a cylindrical porous chamber was extended by the authors to account for arbitrary headwall injection. In this study, we construct the solution for the two-dimensional planar case while incorporating variable headwall injection. The resulting representation is especially well sui...

Current ballistics analyses require detailed information of the internal flowfield forming in the combustion chamber of solid rocket motors. In this study, we develop a model applicable to the circular-port motor with slightly tapered grain. A combined geometric configuration is considered in which a straight cylinder is connected to a tapered cone...

Internal flow modeling is a requisite for obtaining critical parameters in the design and fabrication of modern solid rocket motors. In this work, the analytical formulation of internal flows particular to motors with tapered sidewalls is pursued. The analysis employs the vorticity-streamfunction approach to treat this problem assuming steady, inco...

In this paper, we present the performance analysis of a parallel Algebraic Multigrid Solver (AMG) for a finite volume unstructured CFD code. The parallel perform-ance of the AMG is tested against the sequential imple-mentation for a number of grid sizes and partitions in order to evaluate its scalability with increased mesh sizes. The performance i...