### International Workshop on Computational Flow and Transport: Modeling, Simulations and Algorithms (CFT) Session 1

#### Chair: Shuyu Sun

 388 Statistical Inversion of Absolute Permeability in Single Phase Darcy Flow [abstract]Abstract: In this paper, we formulate the permeability inverse problem in the Bayesian framework using total variation (TV) and $\ell_p$ regularization prior. We use the Markov Chain Monte Carlo (MCMC) method for sampling the posterior distribution to solve the ill-posed inverse problem. We present simulations to estimate the distribution for each pixel for the image reconstruction of the absolute permeability. Thilo Strauss, Xiaolin Fan, Shuyu Sun, Taufiquar Khan 32 An enhanced velocity multipoint flux mixed finite element method for Darcy flow on non-matching hexahedral grids [abstract]Abstract: This paper proposes a new enhanced velocity method to directly construct a flux-continuous velocity approximation with multipoint flux mixed finite element method on subdomains. This gives an efficient way to perform simulations on multiblock domains with non-matching hexahedral grids. We develop a reasonable assumption on geometry, discuss implementation issues, and give several numerical results with slightly compressible single phase flow. Benjamin Ganis, Mary Wheeler, Ivan Yotov 124 A compact numerical implementation for solving Stokes equations using matrix-vector operations [abstract]Abstract: In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectored thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., Matlab and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectored operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions. Tao Zhang, Amgad Salama, Shuyu Sun, Hua Zhong 265 Numerical Models for the Simulation of Aeroacoustic Phenomena [abstract]Abstract: In the development of a numerical model for aeroacoustic problems, two main issues arise: which level of physical approximation to adopt and which numerical scheme is the most appropriate. It is possible to consider a hierarchy of physical aproximations, ranging from the wave equation, without or with convective effects, to the linearized Euler and Navier-Stokes equations, as well as a wide range of high-order numerical schemes, ranging from compact finite difference schemes to the discontinuous Galerkin method (DGM) for unstructured grids. For problems in complex geometries, significant hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes, may occur. For example in ducts with sudden changes of area where flow separation occurs in correspondence of sharp edges with a consequent generation of vorticity for viscous effects. To correctly model this coupling, the Navier-Stokes equations, linearized with respect to a representative mean flow, must be solved. The formulation based on Linearized Navier-Stokes (LNS) equations is suitable to deal with problems involving such hydrodynamic-acoustic interactions. The occurrence of geometrical complexities, such as sharp edges, where acoustic energy is transferred into the vortical modes for viscous effects, requires an highly accurate numerical scheme with non only reduced dispersive properties, to accurate model the wave propagation, but also providing a very low level of numerical dissipation on unstructured grids. The DGM is the most appropriate numerical scheme satisfying these requirements. The objective of the present work is to develop an efficient numerical solution of the LNS equations, based on a DGM on unstructured grids. To our knowledge, there is only one work dealing with the solution of the LNS for aeroacoustics where the equations are solved in the frequency domain. In this work we develop the method in the time domain. The non-dispersive and non-diffusive nature of acoustic waves propagating over long distances forces us to adopt highly accurate numerical methods. DGM is one of the most promising scheme due to its intrinsic stability and to its capability to treat unstructured grids. Both advantages make this method well suited for problems characterized by wave propagation phenomena in complex geometries. The main disadvantage of DGM is the high computational requirements because the discontinuous character of the method which adds extra nodes on the interfaces between cells respect to a standard continuous Galerkin Method (GM). Techniques of optimization of the DGM in the case of the Navier-Stokes equations, to reduce the computational effort, are currently object of intense research. At our knowledge, no similar effort is made in the context of the solution of the LNS equations. The LNS equations are derived and the DGM is presented. Preliminary results for the case of the scattering of plane waves traveling in a duct with a sudden area expansion and a comparison between LEE and LNS calculations of vortical modes, are presented. Renzo Arina

### International Workshop on Computational Flow and Transport: Modeling, Simulations and Algorithms (CFT) Session 2

#### Chair: Shuyu Sun

 56 Numerical simulation of the flow in the fuel injector in sharply inhomogeneous electric field [abstract]Abstract: The results of detailed numerical simulation of the flow in an injector including electrohydrodynamic interaction in sharply inhomogeneous electric field formed by electrode system closed to the “needle-plane” type are presented. The aim of the simulation is to estimate the charge rate flow at the fuel injector outlet. The results were obtained using the open-source package OpenFOAM in which the corresponding models of electrohydrodynamics were added. The parametric calculations were performed for axis-symmetric model using RANS k-omega SST turbulence model. Due to swirl device in fuel injector the flow is strongly swirling. To obtain parameters for axis-symmetric flow calculations the 3D simulation was performed for the simplified injector model including swirl device and without electrods. Alexander Smirnovsky, Vladimir Nagorny, Dmitriy Kolodyazhny, Alexander Tchernysheff 122 An algorithm for the numerical solution of the pseudo compressible Navier-Stokes equations based on the experimenting fields approach [abstract]Abstract: In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique. Amgad Salama, Shuyu Sun, Mohamed El Amin 462 Pore network modeling of drainage process in patterned porous media: a quasi-static study [abstract]Abstract: This work represents a preliminary investigation on the role of wettability conditions on the flow of a two-phase system in porous media. Since such eects have been lumped implicitly in relative permeability-saturation and capillary pressure-saturation relationships, it is quite challenging to isolate its eects explicitly in real porous media applications. However, within the framework of pore network models, it is easy to highlight the effects of wettability conditions on the transport of two-phase systems. We employ quasi-static investigation in which the system undergo slow movement based on slight increment of the imposed pressure. Several numerical experiments of the drainage process are conducted to displace a wetting fluid with a non-wetting one. In all these experiments the network is assigned dierent scenarios of various wettability patterns. The aim is to show that the drainage process is very much aected by the imposed pattern of wettability. The wettability conditions are imposed by assigning the value of contact angle to each pore throat according to predefined patterns. Tao Zhang, Amgad Salama, Shuyu Sun and Mohamed El Amin

### International Workshop on Computational Flow and Transport: Modeling, Simulations and Algorithms (CFT) Session 3

#### Chair: Shuyu Sun

 123 Numerical Treatment of Two-Phase Flow in Porous Media Including Specific Interfacial Area [abstract]Abstract: In this work, we present a numerical treatment of the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which could reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes together with the CCFD and shifting-matrices techniques. Selected simulation results such as $p_c-S_w-a_{wn}$ surface have been introduced. The simulation results have a good agreement with those in the literature using either pore network modeling or Darcy scale modeling. Mohamed El-Amin, Redouane Meftah, Amgad Salama, Shuyu Sun 210 Chaotic states and order in the chaos of the paths of freely falling and ascending spheres [abstract]Abstract: The research extends and improves the parametric study of "Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid" of Jenny et al. (2004) with special focus on the onset of chaos and on chaotic states. The results show that the effect of density ratio responsible for two qualitatively different oblique oscillating states has a significant impact both on the onset of chaos and on the behavior of fully chaotic states. The observed difference between dense and light spheres is associated to the strength of coupling between fluid and solid degrees of freedom. While the low frequency mode of oblique oscillating state presents specific features due to a strong solid - fluid coupling, the dynamics of the high frequency mode is shown to be driven by the same vortex shedding as the wake of a fixed sphere. The different fluid-solid coupling also determines two different ways how chaos sets in. Two outstanding ordered regimes are evidenced and investigated in the chaotic domain. One of them, characteristic for its helical trajectories, might provide a link to the experimentally evidenced, but so far numerically unexplained, vibrating regime of ascension of light spheres. For fully chaotic states, it is shown that statistical averaging converges in a satisfactory manner. Several statistical characteristics are suggested and evaluated. Wei Zhou and Jan Dušek 288 Switching Between the NVT and NpT Ensembles Using the Reweighting and Reconstruction Scheme [abstract]Abstract: Recently, we have developed several techniques in order to accelerate Monte Carlo (MC) molecular simulations. For that purpose, two strategies were followed. In the first, new algorithms were proposed as a set of early rejection schemes performing faster than the conventional algorithm while preserving the accuracy of the method. On the other hand, a reweighting and reconstruction scheme was introduced that is capable of retrieving primary quantities and second derivative properties at several thermodynamic conditions from a single MC Markov chain. The latter scheme, was first developed to extrapolate quantities in NVT ensemble for structureless Lennard-Jones particles. However, it is evident that for most real life applications the NpT ensemble is more convenient, as pressure and temperature are usually known. Therefore, in this paper we present an extension to the reweighting and reconstruction method to solve NpT problems utilizing the same Markov chains generated by the NVT ensemble simulations. Eventually, the new approach allows elegant switching between the two ensembles for several quantities at a wide range of neighboring thermodynamic conditions. Ahmad Kadoura, Amgad Salama, Shuyu Sun 185 Coupled modelling of a shallow water flow and pollutant transport using depth averaged turbulent model. [abstract]Abstract: The paper presents a mathematical model of a turbulent river flow based on unsteady shallow water equations and depth averaged turbulence model. The numerical model is based on upwind finite volume method on structured staggered grid. In order to get a stable numerical solution simple-based algorithm was used. Among well-developed models of the river flow proposed approach stands out with its computational efficiency and high quality in describing processes in a river stream. For the main cases of pollution transport in river flows it is essential to know whether the model is appropriate to predict turbulent characteristics of the flow in the open channel. Two computational cases have been carried out to investigating and to applying established model. The first case shows the impact of confluents into generation of turbulence in the river flow and shows that recirculation flows effects on the process of pollutant dispersion in water basins. Driven cavity test case have been carried out to investigate the accuracy of the established method and its applicability to the streams with a complex structure. Alexander V. Starchenko and Vladislava V. Churuksaeva