Dynamics Solver Research Articles

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint-based design optimization requires coupling an adjoint-enabled computational fluid dynamics (CFD) solver with an adjoint-enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, the sensitivity of the linear-stability eigenvalues constitutes an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency and the adjoint-based sensitivity of the transition location with respect to the spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Interactional Aerodynamics of Single Main Rotor Helicopters in Steady Autorotation

Autorotation is an edge case flight regime where, instead of being powered by an engine, a rotorcraft is powered purely by the air moving up through the main rotor as the vehicle descends. In this paper, a full-vehicle UH-60A helicopter is simulated in steady autorotation using both the flight dynamics (FD) code HeliUM-A and the computational fluid dynamics/computational structural dynamics (CFD/CSD) solver CREATE-AVTM Helios. The CFD/CSD simulations model the full-vehicle geometry and are trimmed to an autorotative state that is representative of how the aircraft flies in practice. Despite significant differences in the predicted airloads, both FD and CFD/CSD predictions of the vehicle’s autorotational descent rate were in excellent agreement with available flight test data. CFD/CSD analysis further examined mutual interactions between the helicopter’s rotors and various airframe components. The airframe plays a critical role in determining the aircraft’s autorotational descent rate and its shed wake creates regions of loading loss in the rotor disk. On the other hand, the main rotor induces significant unsteadiness on the airframe loading and creates an effective downforce on the fuselage and stabilator.

One-Way CFD/FEM Analysis of a Fish Cage in Current Conditions

This study explores the hydrodynamic behaviour of a fish cage in a steady current by employing a fluid–structure interaction model with one-way coupling between a fluid solver and a structural model. The fluid field around the fish cage is predicted using a computational fluid dynamics solver, while the stress and deformation of the netting are calculated using finite element structural algorithm with solid elements reflecting their real geometry. The fluid velocity and hydrodynamic pressure are calculated and mapped to the structural analysis model. The fluid–structure interaction model is validated by comparing drag force results with published experimental data at different current conditions. Instead of modelling the netting of the fish cage as porous media or using lumped mass methods, the complete structural model is built in detail. The analysis of the fluid field around the nets shows that the change in the current condition has a limited impact on the flow behaviour, but the increase in the current velocity significantly enhances the magnitude of the drag force. This study reveals a reduction in flow within and downstream of the net, consistent with prior experimental findings and established research. Mechanical analysis shows that knotted nets have better performance than knotless ones, and although fluid pressure causes some structural deformation, it remains within safe limits, preventing material failure.

Numerical investigation on aerodynamic noise of rigid coaxial rotor in forward flight with lift-offset

A computational fluid dynamics (CFD) solver based on Reynolds-averaged Navier–Stokes (RANS) equations and high-efficiency trim model is used to simulate the unsteady aerodynamics of coaxial rotor. Farassat 1 A equations are adopted for predicting rotor far-field aerodynamic noise. Forward flight cases of a two-bladed rigid coaxial rotor in different advance ratios and lift-offsets (LOS) are conducted. Sound pressure histories of different observation points and noise radiation maps are analyzed. Results indicate that, the intensity of rotor thickness noise moves towards the advancing side in the rotor disk plane, with the increase of advance ratio. Due to the superposition effect, the thickness noise of coaxial rotor is symmetrical, which is different with the single rotor. At low advance ratio, loading noise of the rigid coaxial rotor is enhanced near the blade-crossing azimuths caused by the unsteady interaction of the twin rotors. The enhancement turns weak with the increase of advance ratio. At high advance ratio, increasing LOS tends to enhance the rotor-self BVI noise, while weakening the inter-rotor interaction noise. At certain flight states, appropriate LOS can reduce the overall noise radiation intensity of rigid coaxial rotor.

A Machine Learning-Based Approach for Predicting Aerodynamic Coefficients Using Deep Neural Networks and CFD Data

Artificial Intelligence (AI) and Machine Learning (ML) are increasingly being adopted across various fields, including aerodynamics, exhibiting impressive results in complex computational processes and improving prediction accuracy. This study introduces a novel method for airfoil performance assessment through the development and training of a deep Artificial Neural Network (ANN), used for predicting aerodynamic coefficients and pressure distributions, leveraging comprehensive data obtained by using a Computational Fluid Dynamics (CFD) solver. First, an automated CFD solver was developed for obtaining the extensive dataset needed for the effective training of the ANN. The automation process consisted in the generation of a geometry and a mesh, along with the successful integration of the open-source SU2 solver for conducting the aerodynamic simulations, chosen for its versatility and straightforward integration. Once various airfoil analyses were performed and a comprehensive dataset was obtained, data was normalized and the model was trained. Throughout the training process, several model configurations were tested, varying different architectures, hyperparameters and layer settings, until the best-performing layout was chosen. After broad testing and validation, the optimal configuration was identified as being the one to demonstrate the lowest error rates and the most accurate predictions on both training and unseen data, highlighting the model’s generalization capabilities. This Machine Learning-based approach, used as a substitute for traditional methods, provides remarkable accuracy and robustness, capturing complex behaviors and significantly reducing the computational costs associated with CFD simulations.

Characteristics of surface signature generated by an underwater sphere with regular free surface waves

The characteristics of the wake generated by an underwater sphere in the presence of regular free surface waves are investigated. Based on the spectral wave explicit Navier–Stokes equations decomposition strategy, the incident waves are prescribed based on spectral wave models, and the wake characteristics generated by the underwater sphere are determined using a computational fluid dynamics solver. The effects of the wavelength of the surface waves and the Froude number on the wake characteristics are investigated. The results show that the existence of free surface waves can distort the wake patterns, causing them to shift from the classical V-shaped Kelvin wake to an Ω-shape. Analysis of the spectrum indicates that the distortion of wake patterns is mainly determined by the wave–wave interactions.

Wing–antenna interaction reduces odour fatigue in butterfly odour-tracking flight

Flying insects exhibit remarkable capabilities in coordinating their olfactory sensory system and flapping wings during odour plume-tracking flights. While observations have indicated that their flapping wing motion can ‘sniff’ up the incoming plumes for better odour sampling range, how flapping motion impacts the odour concentration field around the antennae is unknown. Here, we reconstruct the body and wing kinematics of a forwards-flying butterfly based on high-speed images. Using an in-house computational fluid dynamics solver, we simulate the unsteady flow field and odourant transport process by solving the Navier–Stokes and odourant advection-diffusion equations. Our results show that, during flapping flight, the interaction between wing leading-edge vortices and antenna vortices strengthens the circulation of antenna vortices by over two-fold compared with cases without flapping motion, leading to a significant increase in odour intensity fluctuation along the antennae. Specifically, the interaction between the wings and antennae amplifies odour intensity fluctuations on the antennae by up to 8.4 fold. This enhancement is critical in preventing odour fatigue during odour-tracking flights. Further analysis reveals that this interaction is influenced by the inter-antennal angle. Adjusting this angle allows insects to balance between resistance to odour fatigue and the breadth of odour sampling. Narrower inter-antennal angles enhance fatigue resistance, while wider angles extend the sampling range but reduce resistance. Additionally, our findings suggest that while the flexibility of the wings and the thorax's pitching motion in butterflies do influence odour fluctuation, their impact is relatively secondary to that of the wing–antenna interaction.

Dynamics of a hot flexible cantilever plate under natural convection heat transfer in a square cavity

This study investigates the fluid-structure interactions of a flapping plate within a square cavity under four distinct boundary conditions, where two opposing walls are heated isothermally, and the others are adiabatic. These configurations are defined as case 1 (cooled side walls), case 2 (cooled top and bottom walls), case 3 (heated bottom and cooled top wall), and case 4 (heated top wall and cooled bottom wall). The effects of non-dimensional parameters, including Rayleigh number (Ra), Cauchy number (Ca), and mass ratio (β) on plate dynamics and convective heat transfer are analyzed. Numerical investigations are executed utilizing the SU2 open-source multi-physics computational fluid dynamics solver, with a fixed Prandtl number (Pr) set at 0.71 and dimensionless temperature difference (ϵ) established at 0.6. The results show that in cases 1 and 4, the plate exhibits no observable unsteadiness, while cases 2 and 3 reveal different oscillatory behavior within certain parameter ranges, including static mode, periodic flapping mode, quasi-periodic flapping mode, and chaotic flapping mode. In particular, the configuration in case 3 possesses higher inherent instability than case 2, causing the earlier onset of Hopf bifurcation. These findings provide valuable insights into the influence of boundary conditions on the behavior of flexible structures in fluid environments, highlighting the critical role of flow instabilities and boundary conditions in determining the dynamic response of the system.

Coupling of Fluid and Particle-in-Cell Simulations of Ambipolar Plasma Thrusters

Ambipolar plasma thrusters are an appealing technology due to multiple system-related advantages, including propellant flexibility and the absence of electrodes or neutralizer. Understanding the plasma generation and acceleration mechanisms is key to improving the performance and capabilities of these thrusters. However, the source and plume regions inside are often simulated separately, and no self-consistent strategy exists which can couple these different simulations together. This paper introduces the MUlti-regime Plasma Equilibrium Transport Solver (MUPETS), a self-consistent coupled model integrating a fluid solver for the plasma dynamics in the source, which are collision-driven, with a kinetic Particle-In-Cell (PIC) code for the plasma dynamics in the magnetic nozzle, which involve expansion across a diverging magnetic field. The methodology begins by solving the plasma source with the classical Bohm condition at the thruster’s throat. The resulting plasma profiles (density, temperature, speed) are input into the PIC code for the magnetic nozzle. The PIC code calculates the plasma plume expansion and determines the electric field at the thruster’s throat. This electric field is then used as a boundary condition in the fluid code, where it replaces the Bohm assumption, and the fluid simulation is repeated. This iterative process continues until convergence. In comparing the MUPETS results with those for an experimental thruster, the plasma densities at the thruster’s throat differed by less than 2–5% between the fluid and PIC regions. The thrust predictions agreed with the experimental trend, and were kept well within the measurement’s uncertainty band. These results validate the effectiveness of the coupling strategy for enhancing plasma thruster simulation accuracy.

Data-Driven Model Predictive Control for Redundant Manipulators With Unknown Model.

The tracking control of redundant manipulators plays a crucial role in robotics research and generally requires accurate knowledge of models of redundant manipulators. When the model information of a redundant manipulator is unknown, the trajectory-tracking control with model-based methods may fail to complete a given task. To this end, this article proposes a data-driven neural dynamics-based model predictive control (NDMPC) algorithm, which consists of a model predictive control (MPC) scheme, a neural dynamics (ND) solver, and a discrete-time Jacobian matrix (DTJM) updating law. With the help of the DTJM updating law, the future output of the model-unknown redundant manipulator is predicted, and the MPC scheme for trajectory tracking is constructed. The ND solver is designed to solve the MPC scheme to generate control input driving the redundant manipulator. The convergence of the proposed data-driven NDMPC algorithm is proven via theoretical analyses, and its feasibility and superiority are demonstrated via simulations and experiments on a redundant manipulator. Under the drive of the proposed algorithm, the redundant manipulator successfully carries out the trajectory-tracking task without the need for its kinematics model.

Modelling of wall-bounded cavitating flow and spray mixing in multi-component environments using the PC-SAFT equation of state

This work introduces a numerical multiphase model for multi-component mixtures, utilizing tabulated data for physical and transport properties across a spectrum of conditions from near-vacuum pressures to supercritical states. The property data are derived using Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), vapor-liquid equilibrium (VLE) calculations, entropy scaling methodologies, and Group Contribution (GC) methods. These techniques accurately reflect the thermodynamic behaviors of real fluids, avoiding the empirical estimation of Equation of State (EoS) input parameters. Implemented in OpenFOAM, the fluid dynamics solver is designed to address the three-dimensional Navier-Stokes equations for multi-component mixtures. The methodology integrates operator splitting to manage hyperbolic and parabolic steps distinctively. Hyperbolic terms are solved using the HLLC (Harten-Lax-van Leer-Contact) solver with temporal integration performed via a third-order Strong-Stability-Preserving Runge–Kutta (SSP-RK3) method. Viscous stress tensor contributions in the momentum equation are handled through an implicit velocity correction equation, while parabolic terms in the energy equation are explicitly solved. The simulation efficiency is further enhanced by adaptive Local Time Stepping and the Immersed Boundary (IB) method, which addresses interactions between the fluid and solid boundaries. Turbulence is resolved using the Wall Adaptive Large Eddy (WALE) model. Applied to high-pressure diesel fuel spray injections into non-reacting (nitrogen) gas environments, the model has been validated against Engine Combustion Network (ECN) data for the Spray-C configuration, featuring a fully cavitating multi-hole orifice. Results demonstrate that the model achieves accurate predictions across a broad range of tested conditions without the need for tuning or calibration parameters.

Numerical Investigation of Bionic Axial Fan used in Split Air Conditioner

Abstract: Bionic axial fan is the main component in the outdoor unit split type room air-conditioner (AC) which impact the cooling and comfort. The present work aims to improve the aerodynamic performances of bionic axial fan by numerical technique. The detailed simulation has been carried out to investigate the aerodynamic performance of bionic axial fan with various design proposals for a detailed investigation and development of a prospective fan design prior to the manufacture and testing of costly prototypes. According to the biological fact that the serrations at the wing improve the acoustics as well the aerodynamic performances, various design modifications performed on the bionic axial fan blade. As the serrations at the trailing edge help to improve the aerodynamic performance, the fan blade design modified to investigate the change in mass flow rate. The flow field is simulated with the finite element Computational Fluid Dynamics (CFD) solver Altair-AcuSolve to analyse the influence of trailing edge serrations on the air flow rate of fan. The three-dimensional (3D) computational domain with SpalartAllmaras (SA) turbulence model is considered to predict the air flow rate. The present computation is carried out for the axial fan speed of 820 rpm. The flow rate is correlated with the test results to validate the CFD modeling approach. The result shows that the trailing edge serrations at the tip of the fan has predicted improvement in flow rate since it alter the length of separation bubble near the trailing edge which also helps to reduce the noise level.

Prediction of Turbulent Boundary Layer Flow Dynamics with Transformers

Time-marching of turbulent flow fields is computationally expensive using traditional Computational Fluid Dynamics (CFD) solvers. Machine Learning (ML) techniques can be used as an acceleration strategy to offload a few time-marching steps of a CFD solver. In this study, the Transformer (TR) architecture, which has been widely used in the Natural Language Processing (NLP) community for prediction and generative tasks, is utilized to predict future velocity flow fields in an actuated Turbulent Boundary Layer (TBL) flow. A unique data pre-processing step is proposed to reduce the dimensionality of the velocity fields, allowing the processing of full velocity fields of the actuated TBL flow while taking advantage of distributed training in a High Performance Computing (HPC) environment. The trained model is tested at various prediction times using the Dynamic Mode Decomposition (DMD) method. It is found that under five future prediction time steps with the TR, the model is able to achieve a relative Frobenius norm error of less than 5%, compared to fields predicted with a Large Eddy Simulation (LES). Finally, a computational study shows that the TR achieves a significant speed-up, offering computational savings approximately 53 times greater than those of the baseline LES solver. This study demonstrates one of the first applications of TRs on actuated TBL flow intended towards reducing the computational effort of time-marching. The application of this model is envisioned in a coupled manner with the LES solver to provide few time-marching steps, which will accelerate the overall computational process.

Mixed material point method formulation, stabilization, and validation for a unified analysis of free-surface and seepage flow

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions.

Effects of Externally Applied Stress on Multiphase Flow Characteristics in Naturally Fractured Tight Reservoirs

Externally applied stress on the rock matrix plays a crucial role in oil recovery from naturally fractured tight reservoirs, as local variations in pore pressure and in-situ tension are expected. The published literature severely lacks in evaluations of the characteristics of hydrocarbons, displaced by water, in fractured reservoirs under the action of externally applied stress. This study intends to overcome this knowledge gap by resolving complex time- and stress-dependent multiphase flow by employing a coupled Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) solver. Extensive three-dimensional numerical investigations have been carried out to estimate the effects of externally applied stress on the multiphase flow characteristics at the fracture–matrix interface by adding a viscous loss term to the momentum conservation equations. The well-validated numerical predictions show that as the stress loading increases, the porosity and permeability of the rock matrix and capillary pressure at the fracture–matrix interface decrease. Specifically, matrix porosity decreases by 0.13% and permeability reduces by 1.3% as stress increases 1.5-fold. Additionally, stress loading causes a decrease in fracture permeability by up to 29%. The fracture–matrix interface becomes more water-soaked as the stress loading on the rock matrix increases, and thus, the relative permeability curves shift to the right.

An explicit dynamics framework suited to highly non-smooth interface behaviors

Dynamic systems, and in particular mechanical structures, may be subjected to non-smooth loadings such as impacts or shocks. Moreover, their behavior itself may exhibit more or less non-smooth evolutions, as when fracture occurs. Therefore, robust simulation models are of interest to capture such behaviors. A particular focus is made herein on time-stepping explicit dynamics schemes to allow efficient simulations, and non-smoothness is embedded within the discrete resolution model, so that robust simulations can be obtained, with a minimum number of numerical parameters. The original contributions of this article lie in the way the non-smooth behavior is formulated to be embedded in an explicit dynamics framework. This study focuses on the solver for dynamics with non-smooth interface behavior, rather than on the behavior models themselves. The applications concern non-smooth interface behaviors at macroscopic scale, between displacement jump on the 2D interface surface with no thickness, and interfacial force distributions acting on the bodies apart the interface. The proposed test cases which can serve as benchmarks for simulation codes, concern in a first step contact and perfectly plastic interface behavior (for illustrative purpose, on a 0D example). The last numerical test deals with contact, friction, fracture and adhesion for an extrinsic perfectly brittle interface behavior, to exemplify the feasibility on a full 3D finite element model.

Dynamic analysis of multi-module floating photovoltaic platforms with composite mooring system by considering tidal variation and platform configuration

Floating Photovoltaics (FPV) are emerging as an innovative technology to utilizing solar energy which advances the exploration of renewable energy technologies in the deep sea. This investigation proposes a novel methodology to verify the feasibility of the designed models in time-domain analysis via the motion responses, the mooring analysis based on the finite element method (FEM) and the airgap analysis, considering a comparison of dynamic responses between the regular hexagon shape and rectangle shape semi-submersible floating photovoltaic platform (FPVP) both combinate the cables and the tensioners mooring system to adapt the tidal variation. Initially, the response amplitude operators (RAOs) of the two configurations of the FPVP numerical models established in AQWA are derived from the frequency-domain analysis. Then, the method of rectifying the RAOs by incorporating additional damping essential to compensating the fluid viscosity due to the limitation of the potential flow theory is verified through comparison with the Computational Fluid Dynamics (CFD) solver. Subsequently, the motion responses of the two conceptualized FPVPs with the composite mooring system under different depths of water are assessed in time-domain analysis through OrcaFlex which regards the cables and tensioners as Morison type based on the FEM theory. Simultaneously, the variations in the air gap of platforms with dissimilar stiffness tensioners are compared to assess the safety of FPV systems under different water depths. The long-term extreme forecast of effective tension force for various return periods derived from the Weibull distribution model is verified. Finally, considering the factors that influence the design and safety of multi-module floating photovoltaics in variable-depth water, this study provides essential guidance for the safe construction technology of semi-submersible FPVPs, serves as a valuable reference for promoting reliable and cost-effective FPV technologies for offshore environments.

Adaptation of the Low Dissipation Low Dispersion Scheme for Reactive Multicomponent Flows on Unstructured Grids Using Density-Based Solvers

Abstract The low dissipation low dispersion (LD2) second-order accurate scheme is effective for scale-resolving simulations in finite volume computational fluid dynamics (CFD) solvers, thanks to its combination of a skew-symmetric split form for convective terms and matrix-valued artificial dissipation fluxes. However, reactive flow simulations face challenges due to steep gradients and varying gas properties. This study replaces the skew-symmetric scheme with the kinetic energy and entropy preserving (KEEP) scheme, utilizing quadratic and cubic split forms for convective terms, enhancing stability. The nonsmooth fluid interfaces in reactive flow simulations necessitate upwind fluxes for reactive scalars to limit total variation (TV), also requiring upwind fluxes for the mixture-dependent internal energy fluxes. Other convective terms use central discretizations from the KEEP scheme, leveraging LD2’s spatial reconstruction to minimize dispersive errors. Numerical assessments show this approach reduces spurious pressure oscillations in single and multicomponent flows. The absolute flux Jacobian for dissipation flux calculation is efficiently computed using an expanded Turkel’s approach for thermally perfect gas mixtures. Partial pressure derivatives are approximated when using the flamelet generated manifolds (FGM) combustion model. The proposed scheme is evaluated through scale-resolving simulations of the Cambridge burner flame SWB1 on an unstructured grid using the density-based solver TRACE, employing both finite rate chemistry (FRC) and FGM combustion models. Comparative analysis with the all-speed SLAU2 scheme shows the superior performance of the proposed scheme in handling turbulent reactive multicomponent flows.

Numerical Analysis of Cavitation Erosion in 316L Steel with CrN PVD Coating.

The erosion process of a 4 μm monolayer CrN coating deposited on 316L stainless steel due to cavitation was investigated using finite element analysis (FEA). To estimate load parameters from cavitation pit geometry resulting from high impact velocity and high strain rate, the explicit dynamic solver was employed. Water microjet impacts at velocities of 100, 200 and 500 m/s were simulated to recreate different cavitation erosion intensities observed in the experiment. The resulting damage characteristics were compared to previous studies on uncoated 316L steel. The relationship between impact velocity and postimpact geometry was examined. Simulations revealed that only impact at 500 m/s can exceed the maximum yield stress of the substrate without penetrating the coating. Subsequent impacts on the same zone deepen the impact pit and penetrate the coating, leading to direct substrate degradation. The influence of impact velocity on the coating degradation process is discussed.

Refactoring the elastic–viscous–plastic solver from the sea ice model CICE v6.5.1 for improved performance

Abstract. This study focuses on the performance of the elastic–viscous–plastic (EVP) dynamical solver within the sea ice model, CICE v6.5.1. The study has been conducted in two steps. First, the standard EVP solver was extracted from CICE for experiments with refactored versions, which are used for performance testing. Second, one refactored version was integrated and tested in the full CICE model to demonstrate that the new algorithms do not significantly impact the physical results. The study reveals two dominant bottlenecks, namely (1) the number of Message Parsing Interface (MPI) and Open Multi-Processing (OpenMP) synchronization points required for halo exchanges during each time step combined with the irregular domain of active sea ice points and (2) the lack of single-instruction, multiple-data (SIMD) code generation. The standard EVP solver has been refactored based on two generic patterns. The first pattern exposes how general finite differences on masked multi-dimensional arrays can be expressed in order to produce significantly better code generation by changing the memory access pattern from random access to direct access. The second pattern takes an alternative approach to handle static grid properties. The measured single-core performance improvement is more than a factor of 5 compared to the standard implementation. The refactored implementation of strong scales on the Intel® Xeon® Scalable Processors series node until the available bandwidth of the node is used. For the Intel® Xeon® CPU Max series, there is sufficient bandwidth to allow the strong scaling to continue for all the cores on the node, resulting in a single-node improvement factor of 35 over the standard implementation. This study also demonstrates improved performance on GPU processors.