Incompressible Smoothed Particle Hydrodynamics Research Articles

A smoothed particle hydrodynamics method for two-phase electrohydrodynamics modeling with Nernst–Planck equations

The widely used leaky dielectric model often overlooks the rate of change in electric charges, leaving the impact of the charge conservation mechanism on two-phase electro-hydrodynamics (EHD) flows inadequately explored. In this study, we address this gap by introducing a charge-conservative model (CCM) for simulating such EHD systems within the framework of the smoothed particle hydrodynamics (SPH) method. Our methodology employs a fully explicit incompressible SPH (EISPH) approach to discretize the pressure Poisson, the electric potential Poisson, and the Nernst–Planck (N–P) equations. This work presents two notable contributions: (i) the introduction of the charge-conservative model into the incompressible SPH framework and (ii) the achievement of its discretization through a fully explicit methodology. To validate the proposed CCM, we conduct a comprehensive comparison with analytical solutions, as well as existing numerical and experimental results. The results affirm that the CCM consistently produces accurate outcomes across various test cases.

An improved incompressible SPH with unified semi-analytical wall boundary conditions for free surface flow

An improved incompressible SPH with unified semi-analytical wall boundary conditions for free surface flow

Semi‐implicit Lagrangian Voronoi approximation for the incompressible Navier–Stokes equations

AbstractWe introduce semi‐implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi‐implicit time marching schemes with the robustness of time‐dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection‐based Arbitrary‐Lagrangian‐Eulerian schemes, we need no remapping stage. A semi‐implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence‐free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi‐phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no‐slip and free‐slip boundary conditions.

Impact of double diffusion on solid particle dispersion in rotated cylinders with nano-enhanced phase change materials

This study introduces an innovative approach that combines the Incompressible Smoothed Particle Hydrodynamics method with Artificial Neural Networks to examine the dispersion of solid particles within rotated circular cylinders filled with nano-enhanced phase change materials. This method addresses the limitations of traditional numerical techniques by improving accuracy in complex geometries and dynamic boundary conditions. The various parameters are examined, including the lengths of low sources in boundary walls Lb, dimensionless time τ, Hartmann number (Ha), Darcy number (Da), thermal radiation parameter (Rd), and Rayleigh number (Ra). The solid particles are initially situated at the center gate between the two circular cylinders, maintained at elevated temperature Th and concentration Ch. Due to the upward direction of convection flow, the solid particles are consistently dispersed into the top circular cylinder. The findings offer valuable insights into the system's behavior. The dispersion of solid particles within the NEPCM is influenced by both τ and Lb, showcasing minimal dispersion for τ≤0.1 and intensified dispersion for τ≥0.2, particularly augmented by larger Lb. The heat capacity ratio (Cr) exhibits a decrease with increasing Lb at multiple time points. A decrease in the Darcy number significantly slows down the dispersion of solid particles because of the substantial resistance posed by the porous medium. As the Rayleigh number increases, there is an enhanced dispersion of solid particles into the upper circular cylinder and heightened temperature distributions. Additionally, the average Nusselt number Nu¯ and Sherwood number Sh¯ decrease with the increase in Lb due to the expansion of low-temperature and concentration source. When the length Lb was increased from 0.25 to 1, Nu¯ and Sh¯ decreased by approximately 76% and 67%, respectively, underscoring the impact of geometric configuration on heat and mass transfer efficiency. The study highlights the effectiveness of the MLP model in predicting Nu¯ and Sh¯ values through graphical analysis, showing significant agreement with the target values. The results demonstrated notable improvements in managing particle dispersion and heat/mass transfer, emphasizing the potential of this integrated approach for applications in thermal management and energy optimization.

Revolutionizing bioconvection: Artificial intelligence-powered nano-encapsulation with oxytactic microorganisms

Using incompressible smoothed particle hydrodynamics (ISPH), this study examines the bioconvection flow of oxytactic microorganisms in a porous annulus populated by nano-encapsulated phase change material (NEPCM). Artificial neural network (ANN) is joined with the ISPH method to accurately predict the values of average Nu‾. Between the outside hexagonal-shaped domain and the embedded wavy cylinder, a new annulus is produced. The ranges of the pertinent parameters are wave amplitude of an embedded cylinder A=0.1−0.5, Hartmann number Ha=0−80, a radius of the cylinder Rcyld=0.05−0.5, Darcy number Da=10−2−10−5, undulation number Kund=2−32, bioconvection Rayleigh number Rab=1−1000, Rayleigh number Ra=103−106, and Lewis number Le=1−20. The regulated geometric characteristics of an embedded wavy cylinder, such as wavy amplitude, cylinder radius, and undulation numbers, have been found to contribute significantly to widening the cooling region and minimizing the oxytactic microorganisms. Hence, the embedded wavy cylinder can be applied for various thermal uses including cooling devices and heat exchangers. The average Nu‾ is enhanced under an increment in the geometric parameters of the embedded cylinder. Increasing Rayleigh/bioconvection Rayleigh numbers enhances the buoyancy forces that accelerate the velocity field.

The time‐fractional ISPH method for fin circular rotation on MHD bioconvection flow of oxytactic microorganisms and NEPCM within a hexagonal‐shaped cavity

AbstractThis work investigates the bioconvection flow of oxytactic microorganisms and nanoparticle‐enhanced phase change material (NEPCM) within a hexagonal‐shaped cavity containing a rotated cross fin, utilizing the incompressible smoothed particle hydrodynamics (ISPH) method based on a time‐fractional derivative. The study considers the circular rotation of an inner cross fin and the presence of two rectangular heat sources on the plane walls inside the hexagonal cavity. The novelty of this work is its integration of a hexagonal‐shaped cavity with a rotated cross fin and the use of a time‐fractional derivative in the ISPH method to analyze bioconvection flow, offering new insights into the interaction between microorganism motion and heat transfer dynamics in complex geometries. The effects of Darcy, Hartmann, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on isotherms, heat capacity ratio, microorganism density, velocity fields, and average Nusselt number are analyzed. The key findings demonstrate the significant impact of Rayleigh and bioconvection Rayleigh numbers in enhancing heat distribution and velocity fields, thereby significantly influencing microorganism motion. Due to Lorentz forces, the velocity field decreases by with an increase in the Hartmann number from 0 to 50. The resistance of the nanofluid's velocity becomes apparent as the Darcy number decreases. Increasing Lewis and Péclet numbers cause the microorganisms to shift towards the cavity's boundaries.

The magnetic field on the bioconvection flow of NEPCM in A Z-shaped cavity containing three circular cylinders

This work adopts an incompressible smoothed particle hydrodynamics (ISPH) method for handling the bioconvection flow of nanoparticle-enhanced phase change materials (NEPCM) inside a Z-shaped containing three circular cylinders and oxytactic microorganisms. The fractional time derivative of a system of controlling equations is solved by the ISPH method. The influences of magnetic field on thermosolutal convection of NEPCM in Z-shaped cavity. The mesh-free nature of the ISPH method helps in simulating the nanofluid flow in complex geometries. The Z-shaped cavity was chosen in this work for bioconvection flow because of its uses in semiconductors in solar cells, electronic devices, biomedicine, and thermal batteries. The bioconvection flow and heat transfer of the embedded circular cylinders are significant in heat exchangers and renewable energies. The scales of physical parameters are bioconvection Rayleigh number Rab=1−1000, Lewis number Le=1−20, Hartmann number Ha=0−80, fractional-time derivative α=0.9−1, Rayleigh number Ra=103−106, the radius of embedded circular cylinders Rc=0.05−0.2, and nanoparticles’ parameter ϕ=0−0.15. The results introduced the importance of Rab in enhancing the distributions of oxytactic microorganisms, and oxygen concentrations as well as the intensity of the velocity field. The size of embedded circular cylinders is effective in adjusting the distributions of oxytactic microorganisms, oxygen concentration, and temperature inside a Z-shaped cavity. The maximum velocity field decreases by 86.79 % as nanoparticle concentration increases from 0 % to 15 % due to the resulting high viscosity of the suspension fluid. An expanded radius of embedded circular cylinders improves the values of Nu‾ and Sh‾. This research provides crucial insights into optimizing thermal management and efficiency across diverse technological applications, from electronics to renewable energy and biomedical devices.

Heat and mass transfer dynamics in curved Ш-Chip: ISPH simulations and ANN analysis

This research investigates heat and mass transfer behavior in nano-enhanced phase change materials (NEPCM) within reactive systems using incompressible smoothed particle hydrodynamics (ISPH) coupled with artificial neural network (ANN) predictions. It introduces a novel model comprising six vertical rods and one curved rod, forming a unique Ш-Chip configuration. The complexity of the NEPCM model demonstrates its relevance in fluid dynamics and heat transfer analyses applicable across diverse fields including food processing, electronics cooling, chip manufacturing, heat exchangers, and solar energy systems. The study explores the influence of various dimensionless parameters such as the Frank-Kamenetskii number (Fk), Hartmann number (Ha), Soret and Dufour numbers (Sr&Du), Lewis number (Le), Rayleigh number (Ra), and fractional order parameter (α) on heat and mass transfer phenomena. Heat/mass sources from embedded vertical and curved rods filled with NEPCM are considered within the model. An artificial neural network (ANN) model employing a multilayer perceptron (MLP) structure is utilized to accurately predict the average Nusselt (Nu‾) and Sherwood (Sh‾) numbers, demonstrating its applicability in fluid dynamics and heat transfer analyses. Key insights highlight the role of Fk and Ra in enhancing convection flow and nanofluid velocity within the curved Ш-Chip. Furthermore, variations in Ha lead to observable velocity reductions due to intensified Lorentz forces, while increased Le values result in decreased velocities as thermal diffusion becomes dominant. The fractional order parameter (α) aids in the transition from unsteady to steady state. The unique configuration of the curved Ш-Chip, combined with the incorporation of heat/mass sources from embedded particles, offers promising applications across diverse fields such as food processing, electronics cooling, chip manufacturing, heat exchangers, and solar energy systems. This research underscores the crucial role of understanding the pertinent parameters to ensure the effective development of systems tailored to specific needs. Additionally, it emphasizes the practical value of employing ANN models in predictive modeling to tackle the complexities encountered in engineering applications.

Particle-based modelling of laser powder bed fusion of metals with emphasis on the melting mode transition

The laser-beam powder bed fusion process for metals, commonly abbreviated as PBF-LB/M, is a widely used process for the additive manufacturing of parts. Numerical simulations are useful to identify optimal process parameters for different materials and to obtain detailed insights into process dynamics. The present work uses a single-phase incompressible Smoothed Particle Hydrodynamics (SPH) scheme to model PBF-LB/M which was found to reduce the required computational time and significantly stabilize the partially violent flow in the melt pool in comparison to a weakly compressible SPH approach. The laser-material interaction is realistically modelled by means of a ray tracing method. An approach to model the effective thermal coductivity of the powder bed is proposed. Excellent agreement between the simulation results and experimental X-ray analyses of the transition from conduction melting mode to keyhole mode including geometric properties of the vapor depression zone was found. These results prove the usability of SPH as a high precision simulation tool for PBF-LB/M.Graphic abstract

Employing ISPH simulations and artificial intelligence for enhanced heat and mass transfer in a core reactor with nano-enhanced phase change materials

This research investigates the heat and mass transfer characteristics of nano-enhanced phase change material (NEPCM) within a core reactor, employing both the incompressible smoothed particle hydrodynamics (ISPH) simulations and artificial intelligence (AI) analysis. NEPCM holds promise for enhancing thermal energy storage and transfer efficiency, with applications spanning various fields, including nuclear reactors. Through ISPH simulations, this study delves into the intricate fluid dynamics and phase change phenomena within the reactor, providing valuable insights into the thermal behavior of NEPCM. Eight embedded rods are initially settled inside a reactor with high temperature and concentration on four rods and the others are maintained at low temperature and concentration. The effects of various parameters including the Cattaneo–Christov heat parameter ( δ Heat ) , Cattaneo–Christov mass parameter ( δ Mass ) , Dufour number ( Du ) , Hartmann number ( Ha ) , Soret number ( Sr ) , and thermal radiation ( Rd ) are conducted in this work. δ Heat and δ Mass play critical roles in evaluating heat and mass transfer efficiencies. Raising the Dufour number improves temperature distribution while having a minimal impact on concentration. Additionally, increasing the Dufour number from 0 to 1.5 leads to a 30% increase in the velocity field. Elevating the Soret number significantly enhances velocity and concentration, while increasing the thermal radiation parameter improves temperature distribution. These findings are pertinent across multiple domains like combustion, chemical engineering, and geophysics, aiding in process optimization and system design. The ANN model exhibits high precision in predicting Nusselt and Sherwood numbers, highlighting its effectiveness in forecasting.

Incompressible smoothed particle hydrodynamics simulations enhanced by hybrid artificial intelligence for investigating magnetic field influence on double diffusion in an arc-shaped cavity

Optimizing heat and mass transfer of Nano-Enhanced Phase Change Material (NEPCM) within complex geometries has numerous practical applications across various industries. These include enhancing the performance of heat exchangers, improving the efficiency of solar energy systems, optimizing the cooling of electronic devices, designing more efficient energy systems, and enhancing the processing efficiency in food industry applications. The incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence (AI) are joined to handle the thermosolutal convection of NEPCM inside an arc shape. Different lengths of heat/mass sources are considered in this work. The embedded tree fin is maintained at low temperature and concentration with zero velocities. AI predicted accurately the mean Nusselt and Sherwood numbers by integration with the ISPH simulations that have been done. Heat and mass transmission were investigated for various lengths of partial heat/mass sources, fractional time derivative, Frank-Kamenetskii number, Hartmann number, Rayleigh number, buoyancy ratio parameter, Soret number, Lewis number, and Dufour number. Expanded lengths of heat/mass sources in arc borders improved heat and mass transport inside an arc shape. The fractional time derivative helps in reducing the computing time necessary to achieve a steady state. The Rayleigh number supports the buoyancy forces that raise the velocity field and temperature and concentration distributions inside an arc shape. By including an arc-shaped cooling tree fin, the magnetic field, Lewis number, and buoyancy ratio characteristics are reduced. The Frank-Kamenetskii number contributes to better temperature dispersion. Examples of heat/mass transfer in an arc form with a tree fin include heat exchangers, solar cells, energy systems, electronic device cooling, and food processors.

Magnetic impacts on double diffusion of a non‐Newtonian NEPCM in a grooved cavity: ANN model with ISPH simulations

AbstractEmploying phase change materials (PCMs) offers the advantage of storing and releasing thermal energy while ensuring temperature stability. This characteristic makes PCMs valuable for reducing energy usage across various industrial applications. To explore the magnetic effects on double diffusion of a non‐Newtonian nano‐encapsulated phase change material (NEPCM) in a grooved cavity, the present study combined the incompressible smoothed particle hydrodynamics (ISPH) approach with an artificial neural network (ANN) model. The grooved shape is made up of three constructed grooves: triangular, curved, and rectangular grooves. In the cavity's walls, three segments of boundaries are considered as , , and . The ANN model correctly predicted the mean Nusselt number and Sherwood number when merged with current ISPH simulations. The study's novelty lies in exploring three distinct thermal and mass scenarios regarding double diffusion of a non‐Newtonian NEPCM within an innovative grooved domain. The relevant parameters include the fractional‐time derivative , power‐law index , Rayleigh number , Hartmann number , Soret–Dufour numbers (Sr and Du), and Lewis number Le. The obtained simulations present the significance of distinct boundary conditions in changing the velocity field, heat capacity ratio, temperature, and concentration in a grooved cavity. The fractional parameter accelerates the shift from unstable to steady condition. The increase in from 1.1 to 1.5 results in a 44.5% drop in the velocity maximum. Because of the Lorentz effect of a magnetic field, increasing from 0 to 50 reduces the maximum velocity by 20.9%.

Incompressible Smoothed Particle Hydrodynamics Simulation of Sediment Erosion around Submarine Pipelines

Sediment erosion around submarine pipelines is a popular topic, widely investigated in both ocean and submarine-pipeline engineering. In this paper, the incompressible smoothed-particle hydrodynamics (ISPH) method is modified for simulation of local scouring process around the submarine pipeline under the action of unidirectional flow. The erosion model is based on the Clear Water Particle–Turbid Water Particle–Critical Shear Stress (CWP-TWP-CSS) concept, and a sand–water two-phase model is proposed to deal with the sediment-entrained flow. The results of the numerical simulation are compared with the experimental data to verify the accuracy and applicability of the numerical model. The scouring process around the pipeline is investigated under different conditions, i.e., pipeline diameters, gap ratios, and flow velocities. The ISPH model is further used to study the flow characteristics of the scour pits around the submarine pipeline and the influence of the vortices on the maximum scour depth, to provide a theoretical basis for the stability design of submarine pipelines.

Extreme wave impacts on a suspended box above free surface

A systematic approach incorporating precision-controlled experiments and high-fidelity numerical simulations has been employed to delve deeper into the physics of extreme wave impact pressures. Using a suite of high-speed imaging and high-resolution pressure sensing techniques that are accurately synchronized with the wave generation, a consistent and well-correlated set of data providing details of the focusing incident wave front, flow velocities, and impact pressure time histories has been successfully obtained. The numerical simulations using a validated incompressible smoothed particle hydrodynamics (ISPH) provided further details that were not tractable in the experiments. Based on the results obtained, there were five broad impact scenarios identified, ranging from focusing crest impacts to plunging jet impacts with varying entrapped air. Among these impact types, the highest impact pressures were those associated with a focusing wave crest. It has been found that high impact pressures were correlated with a convergence of the horizontally impinging overturning crest and the vertical surge of the wall boundary water mass, but with the overturning crest impingement just ahead of the arrival of the wall boundary water mass, which in essence amounted to the impingement of a focusing wave front. Depending on the relative arrival times of the impinging crest and the wall boundary upsurge, the impact scenarios could vary from an up-slosh to a jet impingement with a clear entrapped air pocket, followed by a flip-through of the incident crest. For the scenario with the highest impact pressures, broadly classified as type II impact in this paper, the peak pressures could reach as high as 85ρC2, an order of magnitude higher than impact scenarios without the focusing effect, such as the scenario with a plunging jet impact with entrapped air (classified as types III and IV impact in this study). As the volume of entrapped air for this scenario was relatively small, the one-phase ISPH model used in this study was able to capture the peak pressure characteristics, including the peak pressure amplitudes. However, in scenarios with significantly highly entrapped air during impact, a two-phase model would be necessary.

A hybrid method combining ISPH with graph neural network for simulating free-surface flows

The incompressible Smoothed Particle Hydrodynamics (ISPH) is a popular Lagrangian Particle method. In the conventional ISPH method for simulating free-surface flows, the pressure-projection phase, which solves the pressure Poisson's equation (PPE), is the most time-consuming. In this paper, we propose a novel hybrid method by combining the graph neural network (GNN) with the ISPH for modelling the free-surface flows. In the new hybrid method, the graph neural network (GNN) is employed to replace solving the PPE for pressure in the conventional ISPH. To the best of knowledge of the authors, this is the first attempt to combine the GNN with ISPH model in a Lagrangian formulation. The performance of the hybrid method will be evaluated by comparing its results with experimental data, analytical solution or numerical results from other methods for three benchmark test cases: dam breaking, sloshing wave and solitary wave propagation. In addition, the potential of generalization of the hybrid method will be studied by applying it with the GNN model trained on data for relatively simple cases to simulate more complex cases. It will be demonstrated that the hybrid method does not only give satisfactory results, but also shows good potential of generalization. In addition, the new method will be demonstrated to require the computation time which can be 80 times less than the conventional ISPH for estimating pressure for cases with a large number of particles that is usually needed in the practical free-surface flows simulation using ISPH.

The ISPH simulation of Rayleigh-Taylor instability and multi-phase flow within porous media

The present study applies the incompressible smoothed particle hydrodynamics (ISPH) method to simulate multi-phase flow instabilities, specifically Rayleigh-Taylor instability (RTI) and mixing in a sloshing tank, within various porous media. This study is the first numerical attempt to simulate RTI in diverse porous structures. Porous media are modeled with the non-Darcy approach based on linear and nonlinear factors. The Smagorinsky model is employed to implement turbulence stress. Two validation tests were performed to verify the effectiveness of the ISPH technique, the first evaluating pressure over still water in a tank, the second RTI in free fluid, and excellent agreement was obtained in both tests. The results indicate that porosity parameters play a crucial role in controlling the RTI phenomenon and mixing in the sloshing tank. Low porosity leads to high porous resistance, which significantly reduces RTI development and the mixing processes between the two fluids by hindering the interaction of the heavier and lighter fluids. This study shows the effectiveness of the ISPH method in handling complex interfaces in two-phase mixing flows within porous media.

Comparative study of WCSPH, EISPH and explicit incompressible-compressible SPH (EICSPH) for multi-phase flow with high density difference

This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian–Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and reformulated in the ALE framework. The Explicit Incompressible-Compressible SPH (EICSPH) method, which can handle both compressible and incompressible phases, is developed by combining these two approaches in a fully explicit algorithm. The proposed methods are validated and compared through four benchmark problems including Rayleigh-Taylor instability, hydrostatic, liquid sloshing and dam break problems. Firstly, the stability and accuracy of interface modeling of the three methods were verified through Rayleigh-Taylor instability with small density differences. In the hydrostatic problem with a large density difference, the results from all three methods exhibit good agreement in the pressure distribution. Particularly, EICSPH demonstrates the faster convergence when compared to WCSPH, with EISPH showing fastest convergence overall. In the transient sloshing problem, all three methods quantitatively converged to the experimental results and exhibited good agreement, although slight pressure noise was observed in WCSPH initially. Finally, in the dam break problem, all three methods successfully simulated sharp interfaces without non-physical voids. The temporal variations of pressure and height were well predicted by all three methods, with EISPH showing better conformity to the water-air interface morphology obtained from other incompressible numerical methods compared to WCSPH and EICSPH. Additionally, the impact of air speed of sound was examined in EICSPH, where while the difference in pressure variation at the probe was minimal, differences were observed in energy dissipation and the progression of the free surface due to the air cushion effect.

Adjoined ISPH method and artificial intelligence for thermal radiation on double diffusion inside a porous L-shaped cavity with fins

PurposeThe purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.Design/methodology/approachThe ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.FindingsThe resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.Originality/valueA novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

A consistent second order ISPH for free surface flow

The Incompressible Smoothed Particle Hydrodynamics (ISPH) is now a popular numerical method for modelling free surface flows, in particular the breaking waves and violent wave-structures interaction. The ISPH requires the projection approach, leading to solving a pressure Poisson's equation (PPE). Although the accuracy and convergence of the numerical scheme to discretise the Laplacian operator involved in PPE is critical for securing a satisfactory solution of the PPE, the overall performance of the ISPH is also influenced by other key numerical implementations, including (1) estimation of the viscous terms; (2) calculation of the velocity divergence; (3) discretisation of the boundary conditions for the PPE; and (4) evaluation of the pressure gradient. In our previous paper [29], the quadratic semi-analytical finite difference interpolation scheme (QSFDI), which has a leading truncation error at third order derivatives, has been adopted to discretise the Laplacian operator. In this paper, the QSFDI will be adopted, not only for discretising the Laplacian operator, but also for approximating viscous terms, velocity divergence, boundary conditions and pressure gradient. The performance of the newly formulated consistent second order ISPH is assessed by various cases including the oscillating liquid drop, the wave propagation, and the liquid sloshing. The results do not only demonstrate a second order convergence over a limited range of conditions and a higher computational efficiency, i.e., requiring less computational time to achieve the same accuracy, but also show a better mass/energy conservation property and capacity of reproducing a smooth pressure field, than other ISPH models considered in this study.

Incompressible smoothed particle hydrodynamics solutions of double diffusion of nanoparticle-enhanced phase change materials in vertical mounted circular cylinders

The scheme of incompressible smoothed particle hydrodynamics (ISPH) method is developed to solve the time-conformable systems that control the double diffusion of nanoparticle-enhanced phase change materials (NEPCM) inside two circular cylinders saturated by a porous medium. The use of the time-conformable operator in the ISPH approach for addressing the double diffusion of NEPCM in a new domain is what distinguishes this work. This investigation revealed a comprehensive rate of change that impacts the quickening and slowdown of the monotonicity for the nonlinear systems. The physical parameters are time-conformable operator α , time parameter τ , nanoparticles parameter ϕ , Hartmann number Ha , thermal radiation parameter Rd , Darcy parameter Da , Rayleigh number Ra , and fusion temperature θ f . The principal outcomes of the numerical simulations revealed that the nanofluid flow is slowing down by an augmentation in ϕ , Ha , and Rd . The Rayleigh number is working well in enhancing the nanofluid flow and thermosolutal convection within the two circular cylinders. As a result, variable values of Ra are affecting the phase change material. The fusion temperature parameter controls the position/intensity of the phase change material within the two circular cylinders. Besides, the numerical results indicate the significance of α on the transition process of reaching the steady state. The thermosolutal convection and nanofluid speed are varied with the changes on the time-conformable derivative.