Conventional Computational Fluid Dynamics Research Articles

Dual-Solver Hybrid Computational Approach to Integrated Propulsion Aerodynamics

The demand for high-efficiency air vehicles and the development of distributed electric propulsion systems for aircraft are exposing the need for accurate aerodynamic prediction of multiple integrated propulsion systems. Conventional high-fidelity computational methods are too expensive, and low-cost low-fidelity methods make too many aerodynamic assumptions to be applied to these analyses. Dual-solver hybrid computational fluid dynamics (CFD) methods bridge the gap between these two categories of solvers, but many lack capabilities that are needed for complex vehicles. Recent improvements to the hybrid solver OVERFLOW-CHARM provide efficient and accurate analysis of integrated propulsion systems with hybrid CFD methods, as demonstrated on the wing–propeller system of the AIAA Workshop for Integrated Propeller Prediction. Predictions of propeller thrust are within 1% of conventional CFD data, and wing pressure coefficient distributions agree well with both experimental data and conventional CFD methods. The dual-solver results were obtained at half the computational cost of the full CFD simulation.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

Application of a Gas-Kinetic BGK Scheme in Thermal Protection System Analysis for Hypersonic Vehicles

One major problem in the development of hypersonic vehicles is severe aerodynamic heating; thus, the implementation of a thermal protection system is required. A numerical investigation on the reduction of aerodynamic heating using different thermal protection systems is conducted using a novel gas-kinetic BGK scheme. This method adopts a different solution strategy from the conventional computational fluid dynamics technique, and has shown a lot of benefits in the simulation of hypersonic flows. To be specific, it is established based on solving the Boltzmann equation, and the obtained gas distribution function is used to reconstruct the macroscopic solution of the flow field. Within the finite volume framework, the present BGK scheme is specially designed for the evaluation of numerical fluxes across the cell interface. Two typical thermal protection systems are investigated by using spikes and opposing jets, separately. Both their effectiveness and mechanisms to protect the body surface from heating are analyzed. The predicted distributions of pressure and heat flux, and the unique flow characteristics brought by spikes of different shapes or opposing jets of different total pressure ratios all verify the reliability and accuracy of the BGK scheme in the thermal protection system analysis.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics.

To evaluate hemodynamic markers obtained by accelerated GRAPPA (R= 2, 3, 4) and compressed sensing (R= 7.6) 4D flow MRI sequences under complex flow conditions. The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis, -norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities. 4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation. GRAPPA (R= 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

Influence of Foam Morphology on Flow and Heat Transport in a Random Packed Bed with Metallic Foam Pellets-An Investigation Using CFD.

Open-cell metallic foams used as catalyst supports exhibit excellent transport properties. In this work, a unique application of metallic foam, as pelletized catalyst in a packed bed reactor, is examined. By using a wall-segment Computational Fluid Dynamics (CFD) setup, parametric analyses are carried out to investigate the influence of foam morphologies (cell size and porosity ) and intrinsic conductivity on flow and heat transport characteristics in a slender packed bed made of cylindrical metallic foam pellets. The transport processes have been modeled using an extended version of conventional particle-resolved CFD, i.e., flow and energy in inter-particle spaces are fully resolved, whereas the porous-media model is used for the effective transport processes inside highly-porous foam pellets. Simulation inputs include the processing parameters relevant to Steam Methane Reforming (SMR), analyzed for low ( and high ( flow regimes. The effect of foam morphologies on packed beds has shown that the desired requirements contradict each other, i.e., an increase in cell size and porosity favors the reduction in pressure drop, but, it reduces the heat transfer efficiency. A design study is also conducted to find the optimum foam morphology of a cylindrical foam pellet at a higher , which yields = 0.45, = 0.8. Suitable correlations to predict the friction factor and the overall heat transfer coefficient in a foam-packed bed have been presented, which consider the effect of different foam morphologies over a range of particle Reynolds number, .

A simple hydrodynamic-particle method for supersonic rarefied flows

In the practical aerospace industry, the supersonic rarefied effect presents multiscale characteristics from the near-continuum regime to the free molecular regime. In this paper, a simple hydrodynamic-particle method (SHPM) is proposed to efficiently capture the multiscale properties for the supersonic rarefied flow. To combine the conventional computational fluid dynamics solver with the particle-based method, the weights are theoretically derived from the integral solution of the Boltzmann Bhatnagar–Gross–Krook equation. The present numerical method is validated by test cases of supersonic shock wave structure, Sod shock-tube, and supersonic flow around the circular cylinder. Numerical results demonstrate that the SHPM could capture the multiscale properties from the continuum regime to the rarefied regime.

An automated software for real-time quantification of wall shear stress distribution in quantitative coronary angiography data

BackgroundWall shear stress (WSS) estimated in 3D-quantitative coronary angiography (QCA) models appears to provide useful prognostic information and identifies high-risk patients and lesions. However, conventional computational fluid dynamics (CFD) analysis is cumbersome limiting its application in the clinical arena. This report introduces a user-friendly software that allows real-time WSS computation and examines its reproducibility and accuracy in assessing WSS distribution against conventional CFD analysis. MethodsFrom a registry of 414 patients with borderline negative fractional flow reserve (0.81–0.85), 100 lesions were randomly selected. 3D-QCA and CFD analysis were performed using the conventional approach and the novel CAAS Workstation WSS software, and QCA as well as WSS estimations of the two approaches were compared. The reproducibility of the two methodologies was evaluated in a subgroup of 50 lesions. ResultsA good agreement was noted between the conventional approach and the novel software for 3D-QCA metrics (ICC range: 0.73–0-93) and maximum WSS at the lesion site (ICC: 0.88). Both methodologies had a high reproducibility in assessing lesion severity (ICC range: 0.83–0.97 for the conventional approach; 0.84–0.96 for the CAAS Workstation WSS software) and WSS distribution (ICC: 0.85–0.89 and 0.83–0.87, respectively). Simulation time was significantly shorter using the CAAS Workstation WSS software compared to the conventional approach (4.13 ± 0.59 min vs 23.14 ± 2.56 min, p < 0.001). ConclusionCAAS Workstation WSS software is fast, reproducible, and accurate in assessing WSS distribution. Therefore, this software is expected to enable the broad use of WSS metrics in the clinical arena to identify high-risk lesions and vulnerable patients.

Predicting micro-bubble dynamics with semi-physics-informed deep learning

Utilizing physical information to improve the performance of the conventional neural networks is becoming a promising research direction in scientific computing recently. For multiphase flows, it would require significant computational resources for neural network training due to the large gradients near the interface between the two fluids. Based on the idea of the physics-informed neural networks (PINNs), a modified deep learning framework BubbleNet is proposed to overcome this difficulty in the present study. The deep neural network (DNN) with separate sub-nets is adopted to predict physics fields, with the semi-physics-informed part encoding the continuity equation and the pressure Poisson equation P for supervision and the time discretized normalizer to normalize field data per time step before training. Two bubbly flows, i.e., single bubble flow and multiple bubble flow in a microchannel, are considered to test the algorithm. The conventional computational fluid dynamics software is applied to obtain the training dataset. The traditional DNN and the BubbleNet(s) are utilized to train the neural network and predict the flow fields for the two bubbly flows. Results indicate the BubbleNet frameworks are able to successfully predict the physics fields, and the inclusion of the continuity equation significantly improves the performance of deep NNs. The introduction of the Poisson equation also has slightly positive effects on the prediction results. The results suggest that constructing semi-PINNs by flexibly considering the physical information into neural networks will be helpful in the learning of complex flow problems.

Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics (CFD) solvers, e.g., the cell face reconstruction in the finite-volume method or the curvature computation in the Volume-of-Fluid (VOF) method. The latter showed improvements in terms of accuracy for coarsely resolved interfaces, however at the expense of convergence and symmetry. In this work, a hybrid data-driven approach is proposed, addressing the aforementioned shortcomings. We focus on interface reconstruction (IR) in the level-set method, i.e., the computation of the volume fraction and apertures. In the hybrid data-driven IR, a classification neural network decides based on the local interface resolution whether to use conventional linear IR or neural network IR. The proposed approach improves accuracy for coarsely resolved interfaces and recovers the conventional IR for high resolutions, yielding first order overall convergence. Symmetry is preserved by mirroring and rotating the input level-set grid and subsequently averaging the predictions. The hybrid model is implemented into a CFD solver and demonstrated for two-phase flows. Furthermore, we provide details of floating-point symmetric implementation and computational efficiency.

Equations of state for single-component and multi-component multiphase lattice Boltzmann method

The lattice Boltzmann method is an alternative method for conventional computational fluid dynamics. It has been used for simulating single-phase and multiphase flows and transport phenomena successfully and efficiently. In the current work, single-component and multi-component multiphase systems are studied. A methodology that differentiates between types of fluids is developed. Moreover, an approach for a multi-component multiphase system is developed in which a single distribution function is used regardless of the number of components. The value of the cohesion parameter (Gf) in the multi-component multiphase model becomes unimportant, like the cohesion parameter (Gp) in the single-component multiphase model, because their effects cancel when calculating the cohesion force. The fluids and mixtures are treated as real, so that mixing rules are used for the mixtures. Several types of fluids and mixtures are considered to investigate the capability of the proposed approach in dealing with miscible mixtures in both azeotrope and non-azeotrope situations. The layered Poiseuille flow and falling droplet on a liquid film are presented to evaluate the model developed. We conclude that this methodology can distinguish between different types of fluids when modeling single-component and multi-component multiphase systems.

Prediction of medium-to-coal ratio effect in a dense medium cyclone by using both traditional and coarse-grained CFD-DEM models

Dense medium cyclone (DMC) is the working horse in coal industry. In practice, it is usually operated under constant pressure and the operational conditions (mainly medium-to-coal (M:C) ratio and operational pressure) need to be adjusted according to coal washability data (mainly coal particle size and density distributions). Nonetheless, until now it is still not well understood how the M:C ratio would affect the performance of DMCs especially under the practical conditions. In this work, the effect of M:C ratio is for the first time numerically studied under conditions similar to plant operation by using both traditional and coarse-grained (CG) combined approach of computational fluid dynamics (CFD) and discrete element method (DEM), called as traditional CFD-DEM and CG CFD-DEM, in which the flow of coal particles is modelled by DEM or CG DEM which applies Newton’s laws of motion to individual particles and that of medium flow by the conventional CFD which solves the local-averaged Navier-Stokes equations, allowing consideration of particle–fluid mutual interaction and particle–particle collisions. Moreover, impulse and momentum connection law is used to achieve energy conservation between traditional CFD-DEM and CG CFD-DEM. It is found that under constant pressure, the M:C ratio affects DMC performance significantly. The specific effect depends on coal washability or coal type. Under extremely low M:C ratio, the phenomenon that high-quality coal product is misplaced to reject is successfully reproduced, which has been observed in plants in Australian coal industry and called as “low-density tail”. Moreover, strategies are proposed to mitigate the “low-density tail” phenomenon based on the model.

Reduced order model and global sensitivity analysis for return permeability test

Return Permeability Test (RPT) is a laboratory procedure performed on core plugs for estimating the permeability reduction caused by the invasion of drilling and completion fluids into oil and gas reservoirs. Estimating the damage magnitude (i.e., permeability reduction and percentage of the plugged pore throats) from RPT is critical for accurately analyzing and optimizing wells’ production operations. Several parameters such as the extent and permeability of the invaded zone, production rate, and percentage of the open flow area (i.e., the ratio of the pore throats that remain unplugged after the test to total pore throat area of the rock) affect the estimations from RPT by impacting the pressure drop. Therefore, it is necessary to identify the dominant parameters systematically from the production point of view. Also, the numerical solution of the problem is complex and requires a software package, which often has an expensive CPU run time and might not be efficient for engineers all the time. To this end, we present a systematic global sensitivity analysis (GSA) using the Sobol method for two primary purposes. Firstly, to rank the dominant input variables that affect the variation of the inlet pressure of a core plug with a partially open area and a reduced permeability zone at the flow outlet. Secondly, we develop a reduced-order model (ROM) for this complex problem with a controlled error. As a global sensitivity analysis approach, one advantage of the Sobol technique over the local sensitivity analysis is its ability to account for simultaneous changes of multiple input parameters on the variation of the quantity of interest (QI). Another advantage is that the method can be used to create ROMs even in situations where the governing function is not explicitly known. In this study, we selected four variables as the input parameters of our GSA: the thickness and permeability of the invaded zone ( l f and k f ), production velocity v i , and percentage of the open flow area after the test r o . Since the function governing the relationship between the input and output parameters is not known, a Monte-Carlo simulation is used to carry out the required integrations. For this purpose, a total of 8,000 samples from combinations of the selected input variables are generated. The samples are selected from a range of interest for each variable using the Saltelli sample generation algorithm. Then, computational fluid dynamics (CFD) simulations are conducted on the selected input set to generate pressure (QI) at the core inlet. The results show that the internal cake permeability k f has the most significant impact ( ∼ 32%) on total pressure drop. The second and third most dominant first-order variations are the ratio of open flow area to the total core area r o ( ∼ 15%) and injection velocity v i ( ∼ 13%). Also, the combination (simultaneous changes) of r o and k f has the second most dominant effect between all variables ( ∼ 20%). Finally, we presented a ROM for this problem using the dominant input parameters that account for 96% of the changes in QI, and using several examples demonstrates that the error can be controlled. The result of this study is a model that is mathematically simple and runs much faster than the conventional CFD simulations with reasonable accuracy. It is also a tool to identify and rank the dominant input variables and their interactions regarding their impact on QI variations. The proposed methodology will provide useful guidelines for further analysis of RPT results and provide a simple tool for production engineers. • Estimating filtrate properties from RPT is critical in wells production optimization. • RPT numerical solution is complex and requires a software package in efficient. • Sobol technique is used to rank the importance of impacting parameters. • A reduced-order model (ROM) is presented for RPT. • The results show that the internal cake permeability k f has the most significant impact ( ∼ 32%) on the total pressure drop. • The second dominant impact is from the simultaneous changes of r o and k f . • The third dominant variable is the open flow area at the invaded side of the core. • The forth dominant variable is injection velocity v i .

Adaptive mesh refinement method for the reduction of computational costs while simulating slug flow

Microchannel flow boiling has been the focus of many experimental and numerical investigations due to the high heat transfer coefficients that it can induce. However, experimental research has been limited due to the small scales involved, leading researchers to employ computational fluid dynamics (CFD) simulations to resolve the dearth of research on microchannel flow boiling. Conventional CFD methods use a fine uniform mesh to capture the small scales and gradients, such as the liquid-vapour interface. This method has a large computational cost, and as a result, most research reported in the literature has been limited to two-dimensional axisymmetric domains. An interface-tracking adaptive mesh refinement model was created in this study to overcome the limitation of high computational costs without losing accuracy. This model dynamically refined the mesh only in the regions of interest and allowed a coarser mesh in the rest of the domain. This novel approach was able to recreate previously published results with a maximum error of 6.7%, while using less than 1.6% of the mesh elements. Several simulations were conducted in ANSYS Fluent 19.1 to determine the optimal settings for this new method to maintain accuracy and reduce cell count. These settings were determined as three levels of refinement (δL = 3), four refined cells on either side of the interface (δM = 4), and was implemented every five time steps (δT = 5). Finally, a case study was conducted to illustrate the possibility of simulating two-phase flow in microchannels in three dimensions with this method.

Development of a snowdrift model with the lattice Boltzmann method

We developed a snowdrift model to evaluate the snowdrift height around snow fences, which are often installed along roads in snowy, windy locations. The model consisted of the conventional computational fluid dynamics solver that used the lattice Boltzmann method and a module for calculating the snow particles’ motion and accumulation. The calculation domain was a half channel with a flat free-slip boundary on the top and a non-slip boundary on the bottom, and an inflow with artificially generated turbulence from one side to the outlet side was imposed. In addition to the reference experiment with no fence, experiments were set up with a two-dimensional and a three-dimensional fence normal to the dominant wind direction in the channel center. The estimated wind flow over the two-dimensional fence was characterized by a swirling eddy in the cross section, whereas the wind flow in the three-dimensional fence experiment was horizontally diffluent with a dipole vortex pair on the leeward side of the fence. Almost all the snowdrift formed on the windward side of the two-dimensional and three-dimensional fences, although the snowdrift also formed along the split streaks on the leeward side of the three-dimensional fence. Our results suggested that the fence should be as long as possible to avoid snowdrifts on roads.

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet [23], which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet for a benchmark hypersonic flow involving seven field variables. Specifically we predict five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a “plug-and-play” mode.

A Novel Approach of Unit Conversion in the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesoscopic scale. Hence, applying the LBM method for macroscopic problems requires a proper conversion from the physical scale (conventional units) to the mesoscopic scale (lattice units) and vice versa. The Buckingham π theorem and the principle of corresponding states are the popular methods used for data reductions and unit conversion processes in the LBM. Nevertheless, those methods have some issues, such as difficulty in converting specific quantities, such as thermo-physical properties. The current work uses a novel dimensional analysis method systematically for mapping properties’ units between scales. Moreover, the approach has the flexibility in selecting parameters to ensure the stability of the method of solution. Several benchmark examples are used to evaluate the feasibility and accuracy of the proposed approach. In conclusion, the proposed approach showed the flexibility of the mapping between meso-scale to macro-scales and vice versa on solid bases rather than ad-hoc methods.

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Generative adversarial networks with physical evaluators for spray simulation of pintle injector

Due to the adjustable geometry, pintle injectors are especially suitable for liquid rocket engines, which require a widely throttleable range. However, applying the conventional computational fluid dynamics approaches to simulate the complex spray phenomenon in the whole range still remains a great challenge. In this paper, a novel deep learning approach used to simulate instantaneous spray fields under continuous operating conditions is explored. Based on one specific type of neural network and the idea of physics constraint, a Generative Adversarial Networks with Physics Evaluators framework is proposed. The geometry design and mass flux information are embedded as inputs. After the adversarial training between the generator and discriminator, the generated field solutions are fed into two physics evaluators. In this framework, a mass conversation evaluator is designed to improve the training robustness and convergence. A spray angle evaluator, which is composed of a down-sampling Convolutional Neural Network and theoretical model, guides the networks to generate the spray solutions more closely according to the injection conditions. The characterization of the simulated spray, including the spray morphology, droplet distribution, and spray angle, is well predicted. This work suggests great potential for prior physics knowledge employment in the simulation of instantaneous flow fields.

Deep Learning Framework for Real-Time Estimation of in-silico Thrombotic Risk Indices in the Left Atrial Appendage

Patient-specific computational fluid dynamics (CFD) simulations can provide invaluable insight into the interaction of left atrial appendage (LAA) morphology, hemodynamics, and the formation of thrombi in atrial fibrillation (AF) patients. Nonetheless, CFD solvers are notoriously time-consuming and computationally demanding, which has sparked an ever-growing body of literature aiming to develop surrogate models of fluid simulations based on neural networks. The present study aims at developing a deep learning (DL) framework capable of predicting the endothelial cell activation potential (ECAP), an in-silico index linked to the risk of thrombosis, typically derived from CFD simulations, solely from the patient-specific LAA morphology. To this end, a set of popular DL approaches were evaluated, including fully connected networks (FCN), convolutional neural networks (CNN), and geometric deep learning. While the latter directly operated over non-Euclidean domains, the FCN and CNN approaches required previous registration or 2D mapping of the input LAA mesh. First, the superior performance of the graph-based DL model was demonstrated in a dataset consisting of 256 synthetic and real LAA, where CFD simulations with simplified boundary conditions were run. Subsequently, the adaptability of the geometric DL model was further proven in a more realistic dataset of 114 cases, which included the complete patient-specific LA and CFD simulations with more complex boundary conditions. The resulting DL framework successfully predicted the overall distribution of the ECAP in both datasets, based solely on anatomical features, while reducing computational times by orders of magnitude compared to conventional CFD solvers.

Hybrid Lattice Boltzmann Simulation of Three-Dimensional Natural Convection

The capability of hybrid lattice Boltzmann–finite difference model in simulation of laminar and turbulent three-dimensional (3D) natural convection was examined. Fluid dynamics was computed by means of the lattice Boltzmann method and the finite difference solver was used for advection-diffusion equation. It was found that both two-dimensional and 3D models reproduced the same thermal fields. The Nusselt numbers were in a good agreement with benchmark data with the Rayleigh number up to Computation speed of developed hybrid model was more than two times higher in comparison with conventional computational fluid dynamics (CFD) vorticity–vector potential formulation.