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Publication date: 30 October 2020
Source: Computers & Fluids, Volume 211
Author(s):
Publication date: 30 October 2020
Source: Computers & Fluids, Volume 211
Author(s): Mehdi Mostafaiyan, Sven Wießner, Gert Heinrich
Publication date: Available online 14 September 2020
Source: Computers & Fluids
Author(s): Antonio Posa, Riccardo Broglia, Elias Balaras
Publication date: Available online 27 June 2020
Source: Computers & Fluids
Author(s): Wenqiang He, Guoliang Qin, Yazhou Wang, Zhenzhong Bao
Publication date: Available online 6 August 2019
Source: Computers & Fluids
Author(s): Mehdi Falsafioon, Sina Arabi, Ricardo Camarero, Francois Guibault
Publication date: Available online 13 March 2020
Source: Computers & Fluids
Author(s): Amir Banari, Martin Gehrke, Christian F. Janßen, Thomas Rung
Publication date: 30 October 2020
Source: Computers & Fluids, Volume 211
Author(s): Mathieu Deuse, Richard D. Sandberg
Publication date: 30 October 2020
Source: Computers & Fluids, Volume 211
Author(s): Himakar Ganti, Prashant Khare
Publication date: 15 November 2020
Source: Computers & Fluids, Volume 212
Author(s): Marco Tiberga, Aldo Hennink, Jan Leen Kloosterman, Danny Lathouwers
Publication date: 15 November 2020
Source: Computers & Fluids, Volume 212
Author(s): Jincheng Lou, Jacob Johnston, Nils Tilton
In this paper, we present exact Riemann solvers for the Riemann problem and the half Riemann problem, respectively, for one‐dimensional multi‐material elastic‐plastic flows with the Mie‐Grüneisen equation of state(EOS), hypo‐elastic constitutive model and the von Mises' yielding condition. We firstly analyze the Jacobian matrices in the elastic and plastic states, and then build the relations of different variables across different type of waves. Based on these formulations, an exact Riemann solver is constructed with totally thirty‐six possible cases of wave structures. A large number of tests prove the rightness of the new exact Riemann solver. Moreover, an exact Riemann solver is also deduced for the half Riemann problem and its validity is tested by two examples.
1. We present a new overset assembly method allowing for multiple overlapping bodies by searching the donor cell before identifying the interpolation boundary. 2. It shows good ability to eliminate “isolated island” and “orphan point” problems by selecting interpolation cells only in areas with donor cells. 3. It was properly validated by several cases and the efficiency of the overset assembly was significantly higher than other similar overset assembly programs.
A robust overset assembly method allowing for multiple overlapping bodies is presented. This method extends the overset assembly method to deal with the interference between objects and prevents the failure of the search for donor cells due to the complex shape of the models. The donor cells are searched before identifying the boundary of the chimera interpolation. By selecting interpolation cells only in areas with donor cells, the final overset interpolation boundary cells can always find their donor cells, which prevents orphan points and achieves excellent robustness. First, the implementation of the proposed assembly method is described in detail. Subsequently, the usability and efficiency of the method are verified using several cases. Finally, the integration strategy of the computational fluid dynamics solver based on overset interpolation with the modification of the boundary type is described and verified using practical cases with overlapping bodies. The results demonstrate the applicability of the proposed overset grid assembly method.
A multifield two‐fluid model is proposed, allowing for adaptive switching between different flow morphologies. A compact momentum interpolation method for multiphase flows is applied and virtual mass consistently added to this approach. Large‐scale interfaces are described with an appropriate drag model formulation and the stiff system is approximately resolved with a partial‐elimination algorithm, which is extended to multiple phases via a sum formulation. Solver capabilities are demonstrated in cases, where disperse and multiple continuous phases occur in the same location.
A morphology adaptive modeling framework is derived that is able to handle computationally efficiently dispersed as well as resolved interfacial structures coexisting in the computational domain with the same set of equations. The Eulerian multifield two‐fluid model is combined with the compact momentum interpolation method for multiple phases, which has been proposed in the literature as an extension to the Rhie‐Chow pressure‐velocity coupling. Additionally to the interfacial drag force, the virtual mass force is consistently accounted for in the model. Utilizing a specialized interfacial drag formulation, large interfacial structures can be described with the presented method in a volume‐of‐fluid‐like manner, additionally to the disperse description. The strong phase coupling due to the drag closure model in interfacial regions is resolved with a partial elimination algorithm, which is adapted to work in an approximate manner for more than two phases via a sum formulation. The presented model is implemented in the C++ library OpenFOAM and solver performance is compared with results obtained with the homogeneous model approach in two cases of a single rising gas bubble for two‐ and three‐dimensional space, respectively. Additionally, for both three‐dimensional cases, the results are compared with experimental data. Finally, the presented method's capability of representing dispersed and resolved interfacial structures at the same time is demonstrated with two test cases: a two‐dimensional gas bubble, rising in a liquid, which is laden with micro gas bubbles, and a two‐dimensional stagnant stratification of water and oil, sharing a large‐scale interface, which is penetrated by micro gas bubbles.
Amultiscale computational scheme is developed to use given small micro‐scale simulations of complicated physicalwave processes to empower macro‐scale system‐level predictions. By coupling small patches of simulations over unsimulated space, large savings in computational time are realisable. Here we generalise the patch scheme to the case of wave systems on staggered grids in 2D space. Classic macro‐scale interpolation provides a generic coupling between patches that achieves consistency between the emergent macro‐scale simulation and the underlying micro‐scale dynamics. Spectral analysis indicates that the resultant scheme empowers feasible computation of large macro‐scale simulations of wave systems even with complicated underlying physics. As a example of the scheme’s application, we use it to simulate some simple scenarios of a given turbulent shallow water model.
Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to non‐entropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This paper proposes a simple, robust, and accurate hybrid Roe scheme (Roe^{+} scheme) by hybridizing the Roe scheme and the modified AUSMV^{+} scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd‐even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.
This paper demonstrates the capability of the MPFA‐D, coupled with a hybrid‐grid scheme, to model two‐phase flows in a naturally fractured porous media, with channels or barriers in different spatial positions, using unstructured grids, under any permeability tensors.
Two‐phase flows of oil and water in naturally fractured reservoirs can be described by a system of nonlinear partial differential equations that comprises of an elliptic pressure equation and hyperbolic saturation equation coupled through the total velocity field. Modeling this problem is a great challenge, due to the complexity of the depositional environments, including inclined layers and fractures with different sizes and shapes, and random spatial distribution. In this work, to solve the pressure equation, we adopted a cell‐centered finite‐volume method with a multipoint flux approximation that uses the “diamond stencil” (MPFA‐D) coupled with a hybrid‐grid method (HyG) to deal with the fractures. The classical first‐order upwind method was used to solve the saturation equation, in its explicit and implicit versions. The MPFA‐D is a very robust and flexible formulation that is capable of handling highly heterogeneous and anisotropic domains using general polygonal meshes. In the strategy developed in this work, the mesh that discretize the domain must fit the spatial position of the fractures, so that they are associated to the control surfaces—as (n − 1)D cells—therefore, the calculation of the fluxes in these control surfaces is dependent on the pressures on fractures and on the adjacent volumes. In HyG, the fractures are expanded to nD in the computational domain. The proposed formulation presented quite remarkable results when compared with similar formulations using classical full pressure support and triangle pressure support methods, or even the with MPFA‐D itself when the fractures are treated as nD geometric entities.
A new method for reducing the computational cost of the unsteady vortex lattice method is introduced. The method reduces the order of computations from O(n ^{2}) to O(n) by utilizing two tree structures in tandem. A number of case studies are analyzed to verify its effectiveness and show how the accuracy/efficiency trade‐off can be controlled.
Two new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time‐saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n·log n) tree methods together results in an O(n) method, called the double‐tree method. Other case studies show that the trade‐off between accuracy and speed can be easily and reliably controlled by the agglomeration cutoff distance. For a flat plate with 5 × 200 panels analyzed over 20 time steps, the double‐tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full‐aircraft analysis within optimization or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.
Simulation of Rayleigh‐Taylor instability problem: The proposed scheme, TCNS, together with an accurate/less dissipative Riemann solver, HLLC, obtains significantly high resolutions for small scales
Reynolds‐averaged Navier‐Stokes simulations based on second‐order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin‐friction drag and aerodynamic heating, as well as in simulations of complex flows such as large‐scale separation and transition. A remedy for this is the development of high‐order schemes, by which numerically induced dissipation and dispersion errors of low‐order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high‐resolution nonlinear shock‐capturing methods. A stencil‐selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third‐order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh‐Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.
In this article, a pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. The proposed method is validated based on the comparison of the pressure fluctuations due to an oscillating water column in a closed tube and a free drop of a liquid block in a tank. The developed code is applied to simulate the compression and expansion of the entrapped air in a dam break flow.
A pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single‐pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.
In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.
Publication date: Available online 9 September 2020
Source: Journal of Computational Physics
Author(s): Elena Bachini, Matthew W. Farthing, Mario Putti
Publication date: Available online 10 September 2020
Source: Journal of Computational Physics
Author(s): Oriol Colomés, Alex G. Main, Léo Nouveau, Guglielmo Scovazzi
Publication date: Available online 10 September 2020
Source: Journal of Computational Physics
Author(s): Jörg Stiller
Publication date: Available online 9 September 2020
Source: Journal of Computational Physics
Author(s): Andrea D. Beck, Jonas Zeifang, Anna Schwarz, David G. Flad
Publication date: Available online 9 September 2020
Source: Journal of Computational Physics
Author(s): Weifeng Zhao, Juntao Huang
Publication date: Available online 5 September 2020
Source: Journal of Computational Physics
Author(s): HuiJie Zhang, WeiBing Zhu, Hong Chen
Publication date: Available online 5 September 2020
Source: Journal of Computational Physics
Author(s): Hiroyuki Fujii, Go Chiba, Yukio Yamada, Yoko Hoshi, Kazumichi Kobayashi, Masao Watanabe
Publication date: Available online 8 September 2020
Source: Journal of Computational Physics
Author(s): Ryan F. Johnson, Andrew D. Kercher
Publication date: Available online 11 September 2020
Source: Journal of Computational Physics
Author(s): Martin Almquist, Eric M. Dunham
Publication date: Available online 11 September 2020
Source: Journal of Computational Physics
Author(s): L. Markeeva, I. Tsybulin, I. Oseledets
Parametrically excited standing waves are observed on a cylindrical fluid filament. This is the cylindrical analog of the Faraday instability in a flat surface or spherical droplet. Using Floquet theory, a linear stability analysis is carried out on a viscous cylindrical fluid surface, which is subjected to a timeperiodic radial acceleration. Viscosity of the fluid has a significant impact on the critical forcing amplitude as well as the dispersion relation of the nonaxisymmetric patterns. The effect of viscosity on the threshold of the pattern with azimuthal wavenumber \(m=1\) shows a different dependence from \(m>1\) . It is also observed that the effect of viscosity is greater on the threshold with higher m.
The physical characteristics and evolution of a largescale helium plume are examined through a series of numerical simulations with increasing physical resolution using adaptive mesh refinement (AMR). The five simulations each model a 1mdiameter circular helium plume exiting into a \((4~\hbox {m})^3\) domain and differ solely with respect to the smallest scales resolved using the AMR, spanning resolutions from 15.6 mm down to 0.976 mm. As the physical resolution becomes finer, the helium–air shear layer and subsequent Kelvin–Helmholtz instability are better resolved, leading to a shift in the observed plume structure and dynamics. In particular, a critical resolution is found between 3.91 and 1.95 mm, below which the mean statistics and frequency content of the plume are altered by the development of a Rayleigh–Taylor (RT) instability near the centerline in close proximity to the plume base. Comparisons are made with prior experimental and computational results, revealing that the presence of the RT instability leads to reduced centerline axial velocities and higher puffing frequencies than when the instability is absent. An analysis of velocity and scalar gradient quantities, and the dynamics of the vorticity in particular, show that gravitational torque associated with the RT instability is responsible for substantial vorticity production in the flow. The gridconverged simulations performed here indicate that very high spatial resolutions are required to accurately capture the nearfield structure and dynamics of largescale plumes, particularly with respect to the development of fundamental flow instabilities.
The mass transport in electrokinetically actuated microchannel flow is interesting when the wall reactions influence the wall potential, thereby affecting the hydrodynamics. This is the first work where the electroosmotic flow is impacted by the chemical reactions. Since the wall potential is nonuniform, we have compared the results of the classical Poisson–Boltzmann equations with the generalized Poisson–Nernst–Planck model and investigated the applicability within the range of the operating conditions of the problem. The results provide fundamental understanding of the velocity profile within the channel and the wall concentration, which is significantly different from the classical species transport. The wall concentration is dependent on the electrokinetic parameters rather than the Reynolds and Peclet number solely. For constant volumetric flow rate, the resultant electroosmotic velocity profile is not parabolic and exhibits higher convection close to the wall, leading to reduced solute polarization. The overall mass transport rate can be enhanced by more than two times with respect to nonelectrical phenomena. The results will be useful in understanding the physics and provide operational knowhow of electrokineticbased applications related to capillary electrophoresis, electrochromatrogaphy and (bio)chemical sensing.
Large scale industrial combustion devices, for example, internal combustion engines, gas turbine combustors, etc., operate under highpressure conditions and utilize a variety of fuels. Unfortunately, the majority of the current numerical combustion modelling approaches are not fully validated for highpressure and the nonunity Lewis number ( \(\hbox {Le} =\) thermal diffusivity/mass diffusivity) effects in premixed turbulent combustion. In any case, a numerical model needs to be checked for the effects of these parameters to guarantee generality of the model. In the present study, these two critical features of the models are numerically explored utilizing fundamental elements of several algebraic flame surface density reaction rate closure models accessible in the open literature. The Lewis number impact is likewise examined utilizing LES of recently published subgrid scale fractal flame surface density model, which indicated acceptable results for high and lowpressure methane fuelled applications. The computed numerical results are compared with an extensive experimental dataset for lean methane and propane fuels featuring various flow and turbulence conditions at operating pressures in the range of 1–10 bar. The quantitative results from most of the selected models do not show the experimentally observed trends at highpressures and for nonunity Le number fuels. Modifications to the models are incorporated to reflect effects of these two important parameters utilizing a broad parametric investigation resulting in a satisfactory agreement with the experimental data.
The equations governing the dynamics of a periodically driven microspheroid in an unsteady viscous fluid at low Reynolds number are derived. Its oscillation properties in the presence/absence of memory forces are reported. The core part of the derivation is a perturbation analysis of motion of a sphere. The calculated solutions match with those available in the literature in the limiting case of a sphere. The dependence of the solutions on shape ( \(\alpha \) ), free oscillation frequency ( \(\omega _0\) ) and particle–fluid density ratio ( \(d_r\) ) is calculated. The maximum amplitude of the oscillations of an oblate spheroid is greater than that of a prolate spheroid, showing that the velocity disturbance for an oblate spheroid is higher in the presence/absence of the memory force. The increase in \(\alpha \) leads to the enhancement(reduction) of amplitude peaks in the case of the oblate (prolate) spheroid in the presence and more dominantly in the absence of the force. There is also a reduction in the amplitude of spheroid oscillations of many multiples due to the presence of the memory force. Stronger oscillation variations are observed on changing \(\omega _0\) or \(d_r\) compared to \(\alpha .\) The variations of the value of the phase are similar for both the spheroids on varying \(\omega _0\) and \(d_r\) , whereas they are reversed on varying \(\alpha .\) The linear scaling of amplitude on \(\alpha \) observed for the spheroids may give insight into the physics, especially regarding the quantum of velocity disturbances due to particle size. The slopes are high in the absence of the force, confirming that the presence of the force increases the resistance of spheroid motion, largely. The dependencies of oscillations on the parameters can be utilized for better separation of particles or for characterizing the suspension. The novelty of the problem and its analytical solutions might have value as tests in software for more complicated and realistic systems and hence strikes a good balance between complication and tractability.
Many previous studies have shown that the fidelity of threedimensional cardiovascular flow simulations depends strongly on inflow and outflow boundary conditions that accurately describe the characteristics of the larger vascular network. These boundary conditions are generally based on lowerdimensional models that represent the upstream or downstream flow behavior in some aggregated fashion. However, the parameters of these models are patientspecific, and no clear technique exists for determining them. In this work, an ensemble Kalman filter (EnKF) is implemented for the purpose of estimating parameters in cardiovascular models through the assimilation of specific patients’ clinical measurements. Two types of models are studied: a fully zerodimensional model of the right heart and pulmonary circulation, and a coupled 0D–1D model of the lower leg. Model parameters are estimated using measurements from both healthy and hypertensive patients, and demonstrate that the EnKF is able to generate distinct parameter sets whose model predictions produce features unique to each measurement set. Attention is also given toward the quality of model predictions made in the absence of direct clinical counterparts, as well as techniques to improve filter robustness against shrinking ensemble covariance.
Many aquatic organisms from copepods to harbor seals are able to detect and respond to flow disturbances. The physiological mechanisms underlying such behavior remain a challenge for current and future research. Here, we propose a simplified flow sensing scenario in which a mobile sensor reorients its heading in response to local flow stimuli, with the goal of tracing the wakes created by oscillating airfoils to their source. Specifically, we engineer a feedback control strategy where the sensory measurements are based on transverse vorticity gradients. Through numerical experiments, we assess the efficacy of the sensor in following topologically distinct wakes. We demonstrate that the strategy is robust to variations in the wake itself, and we arrive at empirical rules that the sensor’s initial position and orientation must satisfy in order to successfully locate the airfoil. We conclude by commenting on the relevance of the model and results to animal behavior and bioinspired underwater robotics. We also discuss current and future opportunities for employing machine learning tools to devise and improve these sensory control strategies.
The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the highdimensional, nonlinear, and multiscale dynamics make realtime feedback control infeasible. Fortunately, these highdimensional systems exhibit dominant, lowdimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, lowrank feature spaces characterizing such complex systems. We present a novel deep learning model predictive control framework that exploits lowrank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity.
We present a systematic approach for determining the optimal actuator location for separation control from input–output response data, gathered from numerical simulations or physical experiments. The Eigensystem realization algorithm is used to extract statespace descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control problem is evaluated by computing the generalized output controllability Gramian. We use the method to analyze highfidelity numerical simulation data of the lift and separation angle responses to a pulse of localized bodyforce actuation from six distinct locations on the upper surface of a NACA 65(1)412 airfoil. We find that the optimal location for controlling lift is different from the optimal location for controlling separation angle. In order to explain the physical mechanisms underlying these differences, we conduct controllability analyses of the flowfield by leveraging the dynamic mode decomposition with control algorithm. These modal analyses of flowfield response data reveal that excitation of coherent structures in the wake benefits lift control, whereas excitation of coherent structures in the shear layer benefits separation angle control.
This study presents two different machine learning approaches for the modeling of hydrodynamic force on particles in a particleladen multiphase flow. Results from particleresolved direct numerical simulations (PRDNS) of flow over a random array of stationary particles for eight combinations of particle Reynolds number ( \({\mathrm {Re}}\) ) and volume fraction ( \(\phi \) ) are used in the development of the models. The first approach follows a twostep process. In the first flow prediction step, the perturbation flow due to a particle is obtained as an axisymmetric superposable wake using linear regression. In the second force prediction step, the force on a particle is evaluated in terms of the perturbation flow induced by all its neighbors using the generalized Faxén form of the force expression. In the second approach, the force data on all the particles from the PRDNS simulations are used to develop an artificial neural network (ANN) model for direct prediction of force on a particle. Due to the unavoidable limitation on the number of fully resolved particles in the PRDNS simulations, direct force prediction with the ANN model tends to overfit the data and performs poorly in the prediction of test data. In contrast, due to the millions of grid points used in the PRDNS simulations, accurate flow prediction is possible, which then allows accurate prediction of particle force. This hybridization of multiphase physics and machine learning is particularly important, since it blends the strength of each, and the resulting pairwise interaction extended pointparticle model cannot be developed by either physics or machine learning alone.