Subgrid Level Research Articles

Sensitivity analysis of a multi-scale biofuel primary atomization simulation tool

The purpose is to produce a benchmarked commercial Volume of Fluid (VOF)-to-Discrete Phase Modeling (DPM) numerical algorithm using an experimental study of high-viscosity jet fuel blend C-3. Where the mesh resolution was too coarse to resolve sufficient gas-liquid interfacial curvature, the solver automatically converted VOF biofuel phase mass, momentum, and energy into the equivalent DPM biofuel phase at the sub-grid scale level. Particular attention herein was given to the sensitivity of the results to various numerical degrees of freedom related to the local criteria for conversion of a biofuel from VOF to DPM. The proliferation of commercial simulation tools mandates detailed parametric evaluations. It was found that, while instantaneous conversion rates were extremely sensitive to conversion criteria, atomization physics were not sensitive to the conversion rate effects. Also, this flow system exhibited an outstanding dependence on simulated azimuthal angle, rendering lower order models ineffective. Data sampling methods and durations, along with mesh resolution, were explored such that a particular set of parameters provided a validated model.

Interface area density model for Large-Eddy Simulation of assisted atomization in fiber regime

In the context of simulating liquid rocket engines (LREs), accurately reproducing the complex combustion chamber environment poses a significant challenge. Recent works have shown that Direct Numerical Simulation has made good progress in achieving the simulation of the whole range of temporal and spatial two-phase flow scales involved. However, due to the computational costs, it is currently out of reach in an industrial context. Large-Eddy Simulations (LES) considerably reduce the computational cost but require modeling the two-phase flow at sub-grid level. A promising approach for such modeling is the interface area density (IAD) approach, which was developed initially for LES of flame fronts and subsequently adapted to Diesel jet atomization to recover spray droplet size distributions. In this method, a subgrid density of interface area is transported with an advection equation, while opportune source terms simulate its growth by breakup or its reduction by coalescence effects. In the context of the LREs assisted atomization, the complex mechanism of the assisted atomization in fiber regime must be taken into account by the subgrid model to recover the correct spray size distribution. The present work proposes a new interface area density evolution modeling for two-phase LES of coaxial assisted atomization in fiber regime. The proposed model focuses on recovering a realistic liquid-gas relative velocity at all the scales, enabling accurate modeling of sub-grid scales by using the IAD as a measure of liquid structure sizes.

Use of effective multiscale cohesive models in the simulation of spall in metal plates

AbstractDuctile fracture of metals is the net result of void nucleation, growth and coalescence mechanisms that operate at the microscale. Optimal scaling analysis provides the analytical form of the effective material law that models the ductile fracture phenomena at the macroscale. The upscaled model of ductile behavior assumes the form of a cohesive relation—surface traction versus displacement—of the power‐law type with well‐defined exponents. In the present work, we demonstrate how the effective cohesive law derived from optimal scaling can be conveniently inserted into macroscale calculations by recourse to cohesive elements. The plastic deformation outside the cohesive elements is of moderate size and can be modeled by means of conventional plasticity models. In particular, the mesh size is dictated by accuracy considerations at the macroscale structural level and is not in any way constrained by microscale features and mechanisms, which happen at the subgrid level and are accounted for by the effective cohesive law. We illustrate the multiscale paradigm by means of spall calculations.

CFD Simulation of Low Speed Turbulent Flow Problems Using Unsteady Rans and Large Eddy Simulation Approach

The present paper focuses on the recent development of an implicit pressure-based finite volume algorithm for numerical solution of Navier Stokes equation in an inertial frame of reference for prediction of unsteady incompressible flow problems. The algorithm uses boundary-conforming, multiblock structured grid with moving boundaries, collocated variable arrangement with momentum equations resolved along cartesian directions, second order accurate spatial and temporal discretisation schemes for the convective fluxes and a pressurevelocity solution strategy. Effect of turbulence is simulated using one of the two different approaches. In the Unsteady Reynolds Averaged (URANS) approach coupled to appropriate eddy viscosity based turbulence models, the Navier Stokes (NS) equations, averaged over the whole range of turbulent length scales of the flow, are solved numerically. On the other hand, in the Large Eddy Simulation (LES) approach, the model filtered 3D NS equations are directly solved for the flow variables to resolve the large scale turbulent motions whereas the transport processes at the fine subgrid scale level only are simulated using simple algebraic turbulence model. The capabilities and limitations of both the cost-effective URANS approach and the relatively expensive but rich in physics LES approach have been demonstrated for few application problems of engineering interest.

Reducing impacts of artificial ponding in modeling salt marshes using a conductivity-formulated subgrid model

The landforms of salt marsh systems are rather complex, with meandering channel networks cutting through low-lying, extensive marsh platforms. Some small-scale topographic details are critical to flooding and draining processes but cannot be reflected in the Digital Elevation Model (DEM) due to limited measurement resolution and vegetation bias. Numerical models need a grid with high enough resolution to capture the small-scale connectivity to correctly model the small-scale flow processes, making the model computationally unaffordable. In this study, we derived a subgrid model, which couples two flow components, one is the regular subgrid model for simulating the subgrid-resolved flows, and the other is a conductivity-formulated porous flow model for modeling small-scale gut flows unresolved at the subgrid level. The model validation was performed using an idealized case with a narrow slot that was unresolved in the coupled flow model. Model results were compared with a slot-resolved regular subgrid model where only surface flows are solved and suggested that, with a proper model parameterization, the coupled flow model is capable of reproducing flooding and draining processes similar to the slot-resolved subgrid model of surface flow. The model was applied to simulating flooding and draining processes in a meso-tidal salt marsh. The model results demonstrate that the coupled subgrid model can be used to reduce the impacts of artificial ponding that usually occur in numerical simulations of salt marshes with numerous narrow gullies and creeks.

Inward swirling flamelet model

A new rotational flamelet model with inward swirling flow through a stretched vortex tube is developed for sub-grid modelling to be coupled with the resolved flow for turbulent combustion. The model has critical new features compared to existing models. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) The effects of vorticity and the related centrifugal acceleration are determined. (iii) The strain rates and vorticity applied at the sub-grid level can be directly determined from the resolved-scale strain rates and vorticity without a contrived progress variable. (iv) The flamelet model is three-dimensional. (v) The effect of variable density is addressed. (vi) The inward swirl is created by vorticity combined with two compressive normal strain components; this feature distinguishes the model from counterflow flamelet models. Solutions to the multicomponent Navier–Stokes equations governing the flamelet model are obtained. By coordinate transformation, a similar solution is found for the model, through a system of ordinary differential equations. Vorticity creates a centrifugal force on the sub-grid counterflow that modifies the molecular transport rates, burning rates, and flammability limits. Sample computations of the inward swirling rotational flamelet model without coupling to the resolved flow are presented to demonstrate the importance of the new features. Premixed, nonpremixed, and multi-branched flame structures are examined. Parameter surveys are made with rate of normal strain, vorticity, Damköhler number, and Prandtl number. The centrifugal effect has interesting consequences when combined with the variable-density field. Flow direction can reverse; burning rates can be modified; flammability limits can be extended.

Three-dimensional, rotational flamelet closure model with two-way coupling

A new flamelet model is developed to be used for subgrid modelling and coupled with the resolved flow description for turbulent combustion. The model differs from current models in several critical ways. (i) Non-premixed flames, premixed flames or multi-branched flame structures are determined rather than prescribed. (ii) The effects of shear strain and vorticity on the flames are determined. (iii) The strain rates and vorticity applied at the subgrid level are directly determined from the resolved-scale strain rates and vorticity without the use of a contrived progress variable. (iv) The flamelet model is three-dimensional without need for assuming axisymmetry or planar geometry. (v) The effect of variable density is addressed in the flamelet model. Solutions to the Navier–Stokes equations and the associated scalar equations governing the flamelet model are obtained without the boundary-layer approximation. By appropriate coordinate transformation, a similar solution is found for the rotational flamelet model, reducing it to a system of ordinary differential equations. Vorticity is shown to create a centrifugal force on the subgrid counterflow that modifies the molecular transport rates and burning rate. Sample computations of the rotational flamelet model without coupling to the resolved flow are presented first to demonstrate the importance of the new features of the model. Scaling laws are presented for relating strain rates and vorticity at the subgrid level to those quantities at the resolved-flow level for coupling with large-eddy simulations or the time-averaged mean-flow level for Reynolds-averaged flows. The time-averaged behaviour of a simple turbulent flow is resolved with coupling to the rotational flamelet model. Specifically, a two-dimensional, multicomponent, time-averaged planar shear layer with variable density and energy release is employed using a mixing-length description for the eddy viscosity. Needs for future study are identified.

Contrast-independent partially explicit time discretizations for multiscale wave problems

In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale problems, where the spatial heterogeneities are at subgrid level and are not resolved. In our previous work Chung et al. (2021) [25], we have introduced contrast-independent partially explicit time discretizations and applied to parabolic equations. The main idea of contrast-independent partially explicit time discretization is to split the spatial space into two components: contrast dependent (“fast”) and contrast independent (“slow”) spaces defined via multiscale space decomposition. Using this decomposition, our goal is to appropriately introduce time splitting such that the resulting scheme is stable and can guarantee contrast-independent discretization under some suitable conditions. In this paper, we propose contrast-independent partially explicitly scheme for wave equations, where the splitting requires a careful design. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (“slow”). This condition requires the second space to be contrast independent. Our approaches identify local features that need implicit treatment and the latter is done on a coarse grid using appropriate splitting algorithms. We note that the proposed work extends our previous work Chung et al. (2021) [25] to wave equations. This extension consists of (1) a different discretization (both spatial and temporal), (2) energy conservation property (instead of energy decay), and (3) a different proof strategy. We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast.

A conservative Eulerian-Lagrangian decomposition principle for the solution of multi-scale flow problems at high Schmidt or Prandtl numbers

The simulation of turbulent flow that involves scalar transport at high Schmidt or Prandtl numbers is a major challenge. Enhanced Schmidt and Prandtl numbers demand an excessive increase in numerical resolution. Otherwise, the accuracy of transport would suffer substantially through unresolved information and numerical diffusion. With the aim of providing an efficient alternative for such applications, this paper presents a simulation method that is based on a novel Eulerian-Lagrangian decomposition principle (ELD) of the transported quantity. Low-pass filtering of the initial scalar quantity field separates it into a smooth low-frequency component and a fine-structured high-frequency component. The low-frequency component is represented and transported according to the Eulerian description by applying the Finite Volume Method (FVM) with a numerical resolution according to the Kolmogorov scale. The high-frequency component is translated into the Lagrangian description by the formation of particles, which are transported in parallel. By exchanging information between the two components, a re-initialisation mechanism ensures that the frequency-based decomposition is maintained throughout the simulation. Such ELD approach combines the efficiency of the FVM with the numerical stability of Lagrangian particles. As a result of the frequency-separation, the latter are by principle limited to zones of small scales and thus effectively complement the FVM. Furthermore, the particle information allows details of the scalar quantity field to be reconstructed that extend into the sub-grid level. By using a mixing layer setup, the proposed method is tested for a range of Schmidt numbers, and the numerical costs are considered and discussed.

Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems

This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these works, we have introduced contrast-independent, partially explicit time discretizations for linear equations. The contrast-independent, partially explicit time discretization divides the spatial space into two components: contrast dependent (fast) and contrast independent (slow) spaces defined via multiscale space decomposition. Following this decomposition, temporal splitting was proposed, which treats fast components implicitly and slow components explicitly. The space decomposition and temporal splitting are chosen such that they guarantees stability, and we formulated a condition for the time stepping. This condition was formulated as a condition on slow spaces. In this paper, we extend this approach to nonlinear problems. We propose a splitting approach and derive a condition that guarantees stability. This condition requires some type of contrast-independent spaces for slow components of the solution. We present numerical results and show that the proposed methods provide results similar to implicit methods with a time step that is independent of the contrast.

Effect of sub-grid wrinkling factor modelling on the large eddy simulation of turbulent stratified combustion

Different flame efficiency function (wrinkling factor) models are compared and tested for the Cambridge stratified flame using Large Eddy Simulations (LES) with an artificially thickened flame approach. Different numerical discretisations and definitions of the outer cut-off length are tested, as different practices exist that can have a strong impact on the results. The Cambridge experiment is chosen since it exhibits a Reynolds number of more than 11,500 and the stratified flame is strongly wrinkled further downstream, making it a challenging configuration for the turbulent (stratified) combustion modelling. The sub-grid level physics have been modelled by four wrinkling factor closures, which rely explicitly on algebraic functions of resolved variables, to analyse the influence of wrinkling factor modelling on the predictions of LES. Many such models have been proposed and were tested successfully – but typically for perfectly premixed flames, using specific discretisations and definitions of the cut-off length or filter width. The present paper shows that the models tested perform well even for stratified combustion, provided that the correct definition for the cut-off length is used, and to a lesser extent, suitable discretisation methodologies are employed.

Predicting Vertical Concentration Profiles in the Marine Atmospheric Boundary Layer With a Markov Chain Random Walk Model.

In an effort to better represent aerosol transport in mesoscale and global-scale models, large eddy simulations (LES) from the National Center for Atmospheric Research (NCAR) Turbulence with Particles (NTLP) code are used to develop a Markov chain random walk model that predicts aerosol particle profiles in a cloud-free marine atmospheric boundary layer (MABL). The evolution of vertical concentration profiles are simulated for a range of aerosol particle sizes and in a neutral and an unstable boundary layer. For the neutral boundary layer we find, based on the LES statistics and a specific model time step, that there exist significant correlation for particle positions, meaning that particles near the bottom of the boundary are more likely to remain near the bottom of the boundary layer than being abruptly transported to the top, and vice versa. For the unstable boundary layer, a similar time interval exhibits a weaker tendency for an aerosol particle to remain close to its current location compared to the neutral case due to the strong nonlocal convective motions. In the limit of a large time interval, particles have been mixed throughout the MABL and virtually no temporal correlation exists. We leverage this information to parameterize a Markov chain random walk model that accurately predicts the evolution of vertical concentration profiles. The new methodology has significant potential to be applied at the subgrid level for coarser-scale weather and climate models, the utility of which is shown by comparison to airborne field data and global aerosol models.

A steady-state EMMS drag model for fluidized beds

Mesoscale structures exist inherently in fluidized beds and hence should be taken into account in the constitutive modeling of the drag force. To account for mesoscale effects, previous efforts have been paid on extending the steady-state Energy-Minimization Multi-Scale (EMMS) model to the sub-grid level by introducing acceleration terms into the force balance equations. The EMMS drag models thereof were normally confined into specific flow regimes. In this work, the definition of the heterogeneity index was refined by incorporating the steady-state force balance between the drag and buoyed weight. A simple derivation thereof agrees well with the filtered drag model. Based on such analysis, we proposed a new drag model by solving the steady-state EMMS equations. As a preliminary validation, this new drag was found to allow successful CFD simulation of flow behavior of fluidized beds covering a broad range of flow regimes.

A-Priori Assessment of Interfacial Sub-grid Scale Closures in the Two-Phase Flow LES Context

Due to the continuous increase in available computing power, the Large Eddy Simulation (LES) of two-phase flows started to receive more attention in recent years. Well-established models from single-phase flows are often used to close the sub-grid scale convective momentum transport and recently some modifications have been suggested to account for the jump of density and viscosity at the interface of multi-phase flows. However, additional unclosed terms in multi-phase flows, which are absent in single-phase flows, often remain ignored. This paper focuses on the crucial gaps in literature, namely the modeling of volume fraction advection and surface tension effects on sub-grid level. An a-priori analysis has been conducted for this purpose, i.e. the Direct Numerical Simulation of an academic two-phase flow configuration (single wobbling bubble in a turbulent background flow) has been explicitly filtered (corresponding to implicit filtering in actual LES) for varying filter width and the corresponding sub-grid terms have been compared to potentially suitable model expressions. Besides other approaches, adequately formulated models based on the scale similarity principle emerged to be promising candidates for both sub-grid volume fraction advection as well as sub-grid surface tension effects. In this context, special attention has to be paid to the secondary filter. Owing to the nature of the quasi-singular surface tension term, surface-weighted filtering may be more appropriate and robust than standard volume filtering.

A computationally efficient subgrid model for coupled surface and groundwater flows

We present the development of a high-efficiency and high-resolution subgrid model for simulating surface water and groundwater interaction in coastal regions. The governing equations are derived based on an assumption of the fully-saturated subsurface flow and a phase-averaging method, in which two phase functions are defined respectively for the surface phase and subsurface phase at the subgrid level. Both the surface water and groundwater processes are modeled by solving the phase-averaged equations on a coarse grid, taking into account the subgrid effects. Model validation with laboratory data indicates that the subgrid model is capable of simulating flow processes within permeable structures. The model was applied to simulating flooding and draining processes and the interaction of surface flows and groundwater flows in a meso-tidal salt marsh. The model results demonstrate that the subgrid model can be used in a complex salt marsh system with numerous narrow channels, creeks and artificial ditches, with accuracy similar to that of the full model running directly on the high-resolution grid, but computational costs can be two orders of magnitude smaller than for the full grid model. Tidal influence on the phreatic surface of the groundwater in the marsh system was discussed.

A coupled level set and volume of fluid method with a re-initialisation step suitable for unstructured meshes

This paper presents a coupling method of the level set and volume of fluid methods based on a simple local-gradient based re-initialisation approach that evaluates the distance function depending on the computational cell location. If a cell belongs to the interface, the signed distance is updated based on a search in the neighbouring cells and an interpolation procedure is applied depending on the local curvature or the sign of the level set function following [41]. The search algorithm does not distinguish between the upwind and downwind directions and hence it is able to be used for cells with an arbitrary number of faces increasing the robustness of the method. The coupling with the volume of fluid method is achieved by mapping the volume fraction field which is advected from the isoface evolution at a subgrid level. Consequently, the coupling with the level set approach is utilised without solving the level set equation. This coupled method provides better accuracy than the volume of fluid method alone and is capable of capturing sharp interfaces in all the classical numerical tests that are presented here.

Research Spotlights

We are fortunate to have three topically diverse papers featured in Research Spotlights in the current issue. The first of these, “Stochastic Sensitivity: A Computable Lagrangian Uncertainty Measure for Unsteady Flows," deals with modeling uncertainties in velocity data for the purpose of quantifying their influence when computing Lagrangian particle trajectories of fluids. One application that author Sanjeeva Balasuriya gives for pursuing this line of research is climate and environmental modeling: ocean and atmospheric models utilize velocity data to understand the movement of such quantities of interest as pollutants and plankton, and the trajectories of these quantities of interest have an impact on the environment and climate. This paper fills a gap in the current literature by addressing specifically the impact of velocity uncertainties---including those due to measurement error, turbulence at subgrid levels, or other effects uncaptured by the model---on trajectories. It offers the reader a “set of rigorous computational tools" to quantify the resulting Lagrangian uncertainties as a “physically interpretable field." The final section contains an extensive discussion in which the author considers connections of this work to uncertainty quantification and illuminates important remaining research directions. The second article, coauthored by Yuanzhao Zhang and Adilson E. Motter, is entitled “Symmetric-Independent Stability Analysis of Synchronization Patterns." The stability of synchronization patterns in complex networks is important to understand because of the “significant ramifications in various biological and technical systems" in the absence of such analysis. The key innovation in the present work is the introduction of a new algorithm to find the finest simultaneous block diagonalization (SBD) for any given set of self-adjoint matrices. This permits the extension of the master stability function (MSF) formalism since the proposed method now allows for the optimal separation of perturbation modes from which the stability of arbitrary synchronization patterns can then be undertaken. The authors provide a convincing demonstration of the strength of the new approach by applying their method to characterize permanently stable chimera-like states in multilayer networks. The paper includes a gentle introduction to matrix $*$-algebras and their relevance in developing the new algorithm; code for the latter is available on a GitHub repository, along with test problems. Importantly, the reader should note the potential for SBD in applications beyond the topic considered here---indeed, the authors suggest it may be relevant in other applications that involve many matrices such as control of network systems and semidefinite programming. The subject of the last of the three articles is extremely timely, as the title “Forecasting Elections Using Compartmental Models of Infection" itself suggests. Authors Alexandria Volkening, Daniel F. Linder, Mason A. Porter, and Grzegorz A. Rempala propose a data-driven mathematical model of the temporal evolution of political opinions during U.S. elections. Key features include the explicit modeling of how states influence each other through a compartmental model of disease dynamics, treating “voting intentions as contagions” that spread between states. Data fitting with polling data is used to specify the values of the parameters in the model, and the model predictions are compared to election outcomes from several recent U.S. elections. The initial model is expanded to a stochastic differential equations model in an effort to capture and quantify uncertainty in a given race. The authors are clear in describing their simplifications in modeling, yet the comparison reveals their forecasting method “performs as well as popular analysts." In the interest of transparency and in an effort to encourage more readers to become engaged in the remaining research questions, all codes and data associated with the article are available to the public. And yes, the authors also provide a link where the reader can find their model's forecast for the 2020 U.S. election!

Toward Incorporation of Membrane Properties Non-Uniformity in Spiral Wound Module Performance Simulators—Effect of Non-Uniform Permeability on Fouling Layer Evolution

A performance simulator of spiral wound membrane (SWM) modules used for desalination is a valuable tool for process design and optimization. The existing state-of-the-art mesoscale simulation tools account for the spatial non-uniformities created by the operation itself (flow, pressure, and concentration distributions) but they assume uniform membrane properties. However, experimental studies reveal that membrane properties are by no means uniform. Therefore, the need arises to account for this non-uniformity in simulation tools thus enabling a systematic assessment of its impact, among other benefits; a first step toward this goal is presented herein. In particular, the issue of an organic fouling layer growing on a membrane with non-uniform permeability is analyzed. Several mathematical treatments of the problem are discussed and indicative results are presented. The concept of fouling layer thickness probability density function is suggested as a means to introduce sub-grid level calculations in existing simulation tools. The analysis leads to the selection of an appropriate methodology to incorporate this effect in the dynamic simulation of fouling layer evolution at the membrane-sheet scale.

Modeling of PEM Fuel Cell Catalyst Layers: Status and Outlook

Computational modeling has played a key role in advancing the performance and durability of polymer electrolyte membrane fuel cells (PEMFCs). In recent years there has been a significant focus on PEMFC catalyst layers because of their determining impact on cost and and durability. Further progress in the design of better performance, cheaper and more durable catalyst layers is required to pave the way for large scale deployment of PEMFCs. The catalyst layer poses many challenges from a modeling standpoint: it consists of a complex, multi-phase, nanostructured porous material that is difficult to characterize; and it hosts an array of coupled transport phenomena including flow of gases, liquid water, heat and charged occurring in conjunction with electrochemical reactions. This review paper examines several aspects of state-of-the-art modeling and simulation of PEMFC catalyst layers, with a view of synthesizing the theoretical foundations of various approaches, identifying gaps and outlining critical needs for further research. The review starts with a rigorous revisiting of the mathematical framework based on the volume averaging method. Various macroscopic models reported in the literature that describe the salient transport phenomena are then introduced, and their links with the volume averaged method are elucidated. Other classes of modeling and simulation methods with different levels of resolution of the catalyst layer structure, e.g. the pore scale model which treats materials as continuum, and various meso- and microscopic methods, which take into consideration the dynamics at the sub-grid level, are reviewed. Strategies for multiscale simulations that can bridge the gap between macroscopic and microscopic models are discussed. An important aspect pertaining to transport properties of catalyst layers is the modeling and simulation of the fabrication processes which is also reviewed. Last but not least, the review examines modeling of liquid water transport in the catalyst layer and its implications on the overall transport properties. The review concludes with an outlook on future research directions.

Models of multicomponent splash bridges in face-on galaxy disc collisions

We use an inelastic particle code with shocks and cooling calculated on a subgrid level to study the gas in direct collisions between galaxy discs. The interstellar media (ISM) of the discs are modeled with continuous thermal phases. The models produce many unique structures, collectively called splash bridges. They range from central bridge discs to swirled sheets, which resemble those observed in interacting galaxies. These morphologies are sensitive to the rotation, relative mass, disc offsets and the gas structure in the discs. In the case of the Taffy galaxies - NGC 12914/15, extensive observations have revealed radio continuum emitting gas, HI gas, hot X-rays from hot diffuse gas and more $H_2$ than exists in the Milky Way coexisting in the bridge. The origins of the $H_2$ and large asymmetric distribution of ISM are not clear. We show that for small disc impact parameters, multiple phases of ISM with densities over many orders of magnitude can be removed from their host galaxies into a Taffy-like bridge. The orientation of the discs initial overlap can have a great effect on the distributions of each phase of ISM. In some cases, the models also predict the creation of a possible `dark galaxy,' a large flat region of dense ISM far from the stellar disc potential of either galaxy.