Large eddy simulation (LES) can be performed using general-purpose flow solvers such as Fluent or OpenFOAM. These solvers typically require regular grids with high orthogonality and low skewness for explicit LES. Consequently, most existing LES studies of indoor airflows rely on structured grids. Given this grid constraint, this paper presents a novel framework that demonstrates how the unique characteristics of indoor airflows make orthogonal, non-body-conformal grids a suitable choice for high-fidelity explicit LES in buildings. First, orthogonal grids enable more accurate spatial discretization than general-purpose flow solvers, enhancing the precision of scale-resolving simulations. Second, staggered grid arrangements ensure pressure–velocity coupling without introducing artificial numerical dissipation. Third, indoor airflow simulations often involve relatively moderate Reynolds numbers and localized geometrical complexity, making the immersed boundary method (IBM) particularly suitable for handling solid boundaries. IBM eliminates the need for complex re-meshing techniques required for body-conformal grids, thereby facilitating simulations of airflow disturbances caused by moving objects, such as doors or human movement. Our main contribution is to define and validate this framework, as well as to test it by modifying an existing incompressible flow solver, REEF3D, originally designed for hydrodynamics. We evaluate the performance of this method through a series of benchmark tests relevant to indoor airflows, including assessments of airflows generated by sliding doors.

In scale-resolving simulations such as Large Eddy Simulations (LES), the spatial discretization scheme of the convective term plays a crucial role in avoiding interference between the numerical errors and the subgrid-scale model. Accurate schemes lead to lower truncation errors and better predictions of turbulent flows without the need for an excessively refined grid. To this end, a new second-order finite-difference scheme (HCDS6) has been developed for incompressible flows and orthogonal staggered grids. Compared to the standard second-order scheme, the new scheme has significantly lower dispersion errors. Compared to existing high-order schemes, the numerical stencil of HCDS6 is more compact, which makes it easier to implement, especially considering boundary conditions around complex geometries using Immersed Boundary Methods (IBM). The HCDS6 scheme conserves the discrete momentum with limited production or dissipation of discrete kinetic energy, which guarantees its numerical stability. Its performance is evaluated using an open-source CFD package called REEF3D. Three benchmarks demonstrate the key properties and performance of the scheme: the convection of an isentropic vortex, the Taylor-Green vortex flow, and turbulent channel flow. Its relatively low dispersion errors, combined with ease of implementation, make the HCDS6 scheme a promising candidate for efficient scale-resolving simulations of turbulent flows.

Obstructive sleep apnea (OSA) is a medical condition characterized by repetitive obstructions in the human upper airways during sleep. Recent estimates from the United States show that the condition impacts 15% to 20% of the adult population. OSA treatment can be subdivided into surgical and non-surgical approaches. Non-surgical approaches such as continuous positive airway pressure (CPAP) devices have the highest success rates when used correctly. However, these approaches have low patient compliance due to the invasive nature of the devices during sleep, leaving surgery as a viable alternative for many. Predicting the outcome of OSA surgery is difficult due to the complex nature of both the airways and the surgeries themselves. CFD modeling of the airways is a helpful way to gain valuable insights into the flow structures and the impact of individual surgeries on the airways. However, CFD is not a viable approach for each patient-specific case due to its time-consuming nature. A pragmatic model has been created to predict the outcome of OSA surgery on a patient-specific basis to produce valid surgical estimates fast to be used by non-CFD engineers. The model transforms the human upper airways into a piping system by applying the hydraulic diameter equation on geometries created from CT scans. This paper aims to validate the use of the hydraulic diameter given by Dh = 4 · (A / Pe), where A is the cross-sectional area and Pe is the wetted perimeter, on the complex geometries of the nasal cavity and to provide a novel equation for the hydraulic diameter in the nasal cavity. The proposed hydraulic diameter equation is given by Dh = CDh · (A / Pe) where CDh is the hydraulic diameter coefficient. Airflow has been simulated through a simplified geometry using CFD to validate the hydraulic diameter and find an updated equation. Pragmatic model simulations using the hydraulic diameter have been compared to the results from CFD simulations to assess the pragmatic model’s accuracy. The results showed that the original hydraulic diameter did not give entirely accurate results and that the novel equation using CDh = 3.71 gave the pragmatic model better accuracy for the validation cases. Tuning the parameter CDh for flow in an OSA patient’s upper airways, the pragmatic model succeeded in quite accurately reproducing the area-averaged pressure in the patient’s upper airways.

An efficient and versatile immersed boundary method (IBM) for simulating fluid-structure interaction (FSI) of compressible viscous flows with a convex rigid body has been developed. The compressible Navier-Stokes equations are discretized by globally fourth order summation-by-parts (SBP) difference operators with built-in stability properties and the classical fourth order explicit Runge-Kutta method. The proposed Cartesian grid-based IBM enforces the solid wall boundary conditions at ghost points. Bilinear interpolation of the flow variables at image points and the solid wall boundary conditions are used to determine the flow variables at three layers of ghost points within the solid body in order to introduce the presence of the body interface in the high order flow computation. FSI of freestream flow at Reynolds number 200 and Mach number 0.25 with an elastically mounted circular cylinder is simulated. The equation of motion of the rigid body is solved by the classical fourth order explicit Runge-Kutta method. The coupling between the fluid and the structure is handled by exchanging the positions, velocities and forces at the fluid-structure interface in each stage. The rate of energy transferred between the fluid and the structure is investigated.

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.

In this paper we present experimental and numerical studies of the electrohydrodynamic stretching of a sub-millimetre-sized salt water drop, immersed in oil with added non-ionic surfactant, and subjected to a suddenly applied electric field of magnitude approaching 1 kV/mm. By varying the drop size, electric field strength and surfactant concentration we cover the whole range of electric capillary numbers (CaE) from 0 up to the limit of drop disintegration. The results are compared with the analytical result by Taylor (1964) which predicts the asymptotic deformation as a function of CaE. We find that the addition of surfactant damps the transient oscillations and that the drops may be stretched slightly beyond the stability limit found by Taylor. We proceed to study the damping of the oscillations, and show that increasing the surfactant concentration has a dual effect of first increasing the damping at low concentrations, and then increasing the asymptotic deformation at higher concentrations. We explain this by comparing the Marangoni forces and the interfacial tension as the drops deform. Finally, we have observed in the experiments a significant hysteresis effect when drops in oil with large concentration of surfactant are subjected to repeated deformations with increasing electric field strengths. This effect is not attributable to the flow nor the interfacial surfactant transport.

A ghost-point immersed boundary method for the compressible Navier-Stokes equations with moving boundaries on fixed Cartesian grids is devised by employing high order summation-by-parts (SBP) difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points using bilinearly interpolated flow variables at mirror points. Simulations for compressible viscous flows induced by a transversely oscillating cylinder in a free-stream and a harmonic in-line oscillating cylinder in an initially quiescent fluid are presented and compared with experiments and incompressible fluid flow simulations obtained with body-conforming grid methods. (C) 2018 Elsevier Ltd. All rights reserved.

We present Large Time Step (LTS) extensions of the Harten-Lax-van Leer (HLL) and Harten-Lax-van Leer-Contact (HLLC) schemes. Herein, LTS denotes a class of explicit methods stable for Courant numbers greater than one. The original LTS method (R.J. LeVeque, SIAM J. Numer. Anal. 22 (1985) 1051–1073) was constructed as an extension of the Godunov scheme, and successive versions have been developed in the framework of Roe's approximate Riemann solver. In this paper, we formulate the LTS extension of the HLL and HLLC schemes in conservation form. We provide explicit expressions for the flux-difference splitting coefficients and the numerical viscosity coefficients of the LTS-HLL scheme. We apply the new schemes to the one-dimensional Euler equations and compare them to their non-LTS counterparts. As test cases, we consider the classical Sod shock tube problem and the Woodward-Colella blast-wave problem. We numerically demonstrate that for the right choice of wave velocity estimates both schemes calculate entropy satisfying solutions.

The purpose of the present study is to conduct a numerical investigation of the flow physics underlying the aeroelastic oscillation of a flexible plate in a channel in order to obtain a better understanding of the mechanism of Obstructive Sleep Apnea Syndrome (OSAS) and snoring. OSAS is a sleep related breathing disorder caused by repetitive collapses of the soft tissues in the upper airways during sleep. A simplified 2D model of fluid-structure interaction (FSI) for the soft palate in the upper airways is developed. In recent years, FSI models have been successfully applied to a wide range of physiological systems in the human body, including the vocal tract [1] and soft palate [2]. The interaction between the inspiratory airflow through nose and mouth with the soft palate is modeled as compressible viscous flow over a cantilevered flexible plate. The fluid motion defined in an Eulerian frame and the flexible plate motion defined in a Lagrangian frame are solved in an arbitrary Lagrangian–Eulerian (ALE) formulation and their interaction is handled using an explicit, two–way coupling strategy where forces and deformations are exchanged between the flow and plate at the end of every time step. The compressible flow field is computed by means of a high order finite difference method. Strict stability and high order accuracy are obtained by employing summation by parts (SBP) difference operators, which are 6th order accurate in the interior and 3rd order accurate near the boundaries [3]. To achieve high accuracy and easy parallelization, the 4th order explicit Runge–Kutta method is applied for time integration. The motion of the plate is obtained by solving a two dimensional model in which a thin flexible plate is clamped at its leading edge and is free at its trailing edge [4]. The plate motion is considered under the constraint of inextensibility. This inextensible plate model is described by another set of equations with an additional momentum forcing which is the result of the interaction with the surrounding fluid. The numerical method for computing the structure equation is based on the finite difference method. A staggered grid procedure in the single Lagrangian coordinate is employed. The plate tension is defined at the interfaces of the grid cells and other variables are defined at the primary grid points in the centers of the grid cells. The mesh adapts to the fluid-structure interface in each time step after the force acting from the fluid on the plate has been used to compute the new deformations of the structure and new grid velocities. The multi block structured grid approach is employed to accommodate geometric flexibility without loss of accuracy at block boundaries. In the present study, an improved version of the structural model is proposed in comparison with [2] to better model the behaviour of the soft palate. The primary aim is to efficiently simulate the interaction between a flexible plate and a compressible viscous fluid flow with comparison of the results for the two structural models. We investigate the performance of this coupled

A ghost-point immersed boundary method is devised for the compressible Navier–Stokes equations by employing high order summation-by-parts (SBP) difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points using bilinearly interpolated flow variables at mirror points. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers.

The interface between two liquids is fully described by the interfacial tension only for very pure liquids. In most cases the system also contains surfactant molecules which modify the interfacial tension according to their concentration at the interface. This has been widely studied over the years, and interesting phenomena arise, e.g. the Marangoni effect. An even more complicated situation arises for complex fluids like crude oil, where large molecules such as asphaltenes migrate to the interface and give rise to further phenomena not seen in surfactant-contaminated systems. An example of this is the “crumpling drop” experiments, where the interface of a drop being deflated becomes non-smooth at some point. In this paper we report on the development of a multiscale method for simulating such complex liquid–liquid systems. We consider simulations where water drops covered with asphaltenes are deflated, and reproduce the crumpling observed in experiments. The method on the nanoscale is based on using coarse-grained molecular dynamics simulations of the interface, with an accurate model for the asphaltene molecules. This enables the calculation of interfacial properties. These properties are then used in the macroscale simulation, which is performed with a two-phase incompressible flow solver using a novel hybrid level-set/ghost-fluid/immersed-boundary method for taking the complex interface behaviour into account. We validate both the nano- and macroscale methods. Results are presented from nano- and macroscale simulations which showcase some of the interesting behaviour caused by asphaltenes affecting the interface. The molecular simulations presented here are the first in the literature to obtain the correct interfacial orientation of asphaltenes. Results from the macroscale simulations present a new physical explanation of the crumpled drop phenomenon, while highlighting shortcomings in previous hypotheses.

We present the Large Time Step (LTS) extension of the Roe scheme and apply it to a standard two-fluid model. Herein, LTS denotes a class of explicit methods that are not limited by the CFL (Courant-Friedrichs-Lewy) condition, allowing us to use very large time steps compared to standard explicit methods. The LTS method was originally developed in the nineteen eighties (LeVeque, 1985), where the Godunov scheme was extended to the LTS Godunov scheme. In the present work, the relaxation of the CFL condition is achieved by increasing the domain of dependence. This might lead to difficulties when it comes to boundary and source terms treatment. We address and discuss these difficulties and propose different ways to treat them. For a shock tube test case, where there are neither source terms nor difficulties associated with the boundaries, the method increases both accuracy and efficiency. For a water faucet test case that includes a source term, the method increases the efficiency, while the accuracy strongly depends on the appropriate treatment of boundary conditions and source terms. (C) 2016 Elsevier Inc. All rights reserved.

In this paper we present the Large Time Step method based on the Roe scheme applied to a standard two-fluid model. The Large Time Step method was originally developed in the nineteen eighties by Randall LeVeque and has enjoyed increasing popularity in the CFD community in recent years due to its attractive features such as increased accuracy and efficiency compared to its standard low time step counterparts. In terms of efficiency and computation time, one of the main disadvantages in common explicit schemes is the limited time step size imposed by the CFL condition. The idea behind the Large Time Step method is to increase the domain of dependence which leads to a relaxation of the CFL condition, allowing us to use Courant numbers larger than one, i.e. using very large time steps compared to standard explicit methods. It is shown that such an approach notably reduces the computation time and increases the accuracy of the solution. However, the idea of increasing the domain of dependence causes difficulties when it comes to boundary treatment, especially in the presence of source terms. In this paper, we describe and address these difficulties. We extend the standard Roe scheme with the Large Time Step method and apply it to the standard two-fluid model for the water faucet test case, focusing on the treatment of the boundary conditions. Furthermore, we compare the performance of the scheme with the classical Roe scheme in terms of computational time.

The behaviour of a single sub-millimetre-size water drop falling through a viscous oil while subjected to an electric field is of fundamental importance to industrial applications such as crude oil electrocoalescers. Detailed studies, both experimental and computational, have been performed previously, but an often challenging issue has been the characterization of the fluids. As numerous authors have noted, it is very difficult to have a perfectly clean water-oil system even for very pure model oils, and the presence of trace chemicals may significantly alter the interface behaviour. In this work, we consider a well- characterized water-oil system where controlled amounts of a surface active agent (Span 80) have been added to the oil. This addition dominates any trace contaminants in the oil, such that the interface behaviour can also be well-characterized. We present the results of experiments and corresponding two-phase- flow simulations of a falling water drop covered in surfactant and subjected to a monopolar square voltage pulse. The results are compared and good agreement is found for surfactant concentrations below the critical micelle concentration.

The Rankine–Hugoniot–Riemann (RHR) solver has been designed to solve steady multidimensional conservation laws with source terms. The solver uses a novel way of incorporating cross fluxes as source terms. The combined source term from the cross fluxes and normal source terms is imposed in the middle of a cell, causing a jump in the solution according to the Rankine–Hugoniot condition. The resulting Riemann problems at the cell faces are then solved by a conventional Riemann solver. We prove that the solver is of second order accuracy for rectangular grids and confirm this by its application to the 2D scalar advection equation, the 2D isothermal Euler equations and the 2D shallow water equations. For these cases, the error of the RHR solver is comparable to or smaller than that of a standard Riemann solver with a MUSCL scheme. The RHR solver is also applied to the 2D full Euler equations for a channel flow with injection, and shown to be comparable to a MUSCL solver.

This paper presents a simplified 2D model of fluid-structure interaction for the soft palate in the upper airways with the potential application to study the basic biomechanical mechanisms of the Obstructive Sleep Apnea Syndrome (OSAS). The interaction between the inhaled air through nose and mouth with the soft palate is modeled as compressible flow over a rigid plate in a channel with a flexible structure attached to the plate. Similar models have successfully been used to model the self-sustained oscillating interaction between the vocal folds and the expiratory airflow in the vocal tract [1]. The method is based on the fourth order Summation by Parts (SBP) [2] finite difference operator in space and the classical fourth order explicit Runge-Kutta method in time for the numerical solution of the compressible flow field. The coupling between the fluid and the structure is handled with an explicit, two-way staggered method where forces and deformations are exchanged between the flow and deformable structure in each time-step. The moving mesh for the fluid domain is handled in an ALE fashion. The inhaled air flow in the pharynx is modeled with the compressible Navier-Stokes equations, and the elastic wave equation is used to model the deformation of the soft palate. The numerical method based on the high order SBP difference operator [3, 4] provides a means to get stable solutions and low dispersion errors on structured grids. A multi-block method is employed to subdivide the computational domain into topologically rectangular regions. The drag and lift forces, the position and the velocity of the elastic part of the soft palate are examined. We plan to compare the computed results with experiments to be done in our laboratory. It is demonstrated that the model is able to reproduce the oscillating behavior of the soft palate during normal breathing conditions under the influence of gravity. Potential application to the prediction of the outcome of surgery for OSAS patients is discussed.

Transmission of natural gas through high pressure pipelines has been modeled by numerically solving the governing equations for one-dimensional compressible flow using implicit finite difference methods. In the first case the backward Euler method is considered using both standard first-order upwind and second-order centered differences for the spatial derivatives. The first-order upwind approximation, which is a one-sided approximation, is found to be unstable for CFL numbers less than 1, while the centered difference approximation is stable for any CFL number. In the second case a cell centered method is considered where flow values are calculated at the midpoint between grid points. This method is also stable for any CFL number. However, for a discontinuous change in inlet temperature, the method is observed to introduce unphysical oscillations in the temperature profile along the pipeline. A solution strategy where the hydraulic and thermal models are solved separately using different discretization techniques is suggested. Such a solution strategy does not introduce unphysical oscillations for discontinuous changes in inlet boundary conditions and is found to be stable for any CFL number. The one-dimensional flow model is validated using operational data from a high pressure natural gas pipeline.

To leverage the last two decades' transition in High-Performance Computing (HPC) towards clusters of compute nodes bound together with fast interconnects, a modern scalable CFD code must be able to efficiently distribute work amongst several nodes using the Message Passing Interface (MPI). MPI can enable very large simulations running on very large clusters, but it is necessary that the bulk of the CFD code be written with MPI in mind, an obstacle to parallelizing an existing serial code. In this work we present the results of extending an existing two-phase 3D Navier-Stokes solver, which was completely serial, to a parallel execution model using MPI. The 3D Navier-Stokes equations for two immiscible incompressible fluids are solved by the continuum surface force method, while the location of the interface is determined by the level-set method. We employ the Portable Extensible Toolkit for Scientific Computing (PETSc) for domain decomposition (DD) in a framework where only a fraction of the code needs to be altered. We study the strong and weak scaling of the resulting code. Cases are studied that are relevant to the fundamental understanding of oil/water separation in electrocoalescers.

A Cartesian grid method has been developed for solving the 2D Euler and NavierStokes equations for inviscid and viscous compressible flow, respectively. Using simplified ghost point treatments, we choose the closest grid points as mirror points of the ghost points. Wall boundary conditions are implemented by imposing symmetry conditions at the ghost points of the embedded boundary. The accuracy of the method has been investigated for various test cases. We show computed examples of supersonic inviscid flow past a diamond-wedge airfoil and a circular cylinder. The method is also tested for supersonic laminar flow over a cylinder, for which the computed skin friction profiles have been used to assess the accuracy. Supersonic laminar flow around a NACA0012 airfoil is computed, and the lift and drag coefficients along with the pressure coefficient profile are compared with the literature. Lastly, supersonic flow around a 2D model of the F-22 fighter aircraft with simulated jet engine outflow is chosen to illustrate the flexibility of the method. For inviscid flow, the results obtained with our simplified ghost point treatments are comparable to results with other more complex Cartesian grid methods. For viscous flow, however, a more accurate treatment of the boundary conditions at body surfaces is needed.