Direct Simulation Research Articles

Nonlinear Vlasov and Fokker-Planck Dynamics in Confined Systems with Drag: A Numerical Study

Abstract We explore numerically the behavior of a one-dimensional many-body system consisting of particles that interact through short range repulsive forces, and are also under the effects of drag forces, and of an external confining potential. The statistical dynamics of systems of this kind exhibits interesting links with the thermostatistical formalism based on the Sq non-additive entropies. In the regime of overdamped motion, these systems admit an effective description in terms of a non-linear Fokker-Planck equation. When the overdamped condition is relaxed, and inertial effects are explicitly taken into account, the system can be described by a Vlasov-like effective mean field dynamics. The Vlasov-like description of this type of systems has been recently investigated in the literature from an analytical point of view. In the present contribution we explore the behaviour of these system numerically, through direct molecular dynamics simulations. We consider examples of systems with four different short range repulsive forces, with a dependence on distance given by exponential, Heaviside, Lorentzian, and Bessel functions. The results of our numerical simulations are fully consistent with the predictions derived from the Vlasov-like mean field description. In particular, we verify that, in the asymptotic limit of large times, the system evolves towards a state exhibiting a spatial distribution of particles that coincides with the stationary solution of an appropriate nonlinear Fokker-Planck equation. This limit spatial distribution has the form of a q-Gaussian.

ThunderBoltz: an open-source direct simulation Monte Carlo Boltzmann solver for plasma transport, chemical kinetics, and 0D modeling

Abstract Plasma-neutral interactions, including reactive kinetics, are often either studied in 0D using ODE-based descriptions, or in multi-dimensional fluid or particle-based plasma codes. The latter case involves a complex assembly of procedures that are not always necessary to test effects of underlying physical models and mechanisms for particle-based descriptions. Here we present ThunderBoltz, a lightweight, publicly available 0D direct simulation Monte Carlo code designed to accommodate a generalized combination of species and arbitrary cross sections without the overhead of expensive field solves. It can produce electron, ion, and neutral velocity distributions in applied AC/DC E-field and/or static B-field scenarios. The code is built in the C++ standard library and includes a convenient Python interface that allows for input file generation (including compatibility with cross section data from the LXCat database), electron transport and reaction rate constant post-processing, input parameter constraint satisfaction, calculation scheduling, and diagnostic plotting. These codes can be accessed at the repository: https://github.com/lanl/ThunderBoltz. In this work we compare ThunderBoltz transport calculations against Bolsig+ calculations, benchmark test problems, and swarm experiment data, finding good agreement with all three in the appropriate field regimes. In addition, we present example use cases where the electron, ion, and background neutral particle species are self-consistently evolved to model the background kinetics, a feature that is absent in fixed-background Monte Carlo and n-term Boltzmann solvers. The latter functionality allows for the possibility of particle-based chemical kinetics simulations of the plasma and neutral species as a new alternative to ODE-based approaches.

Mechanism-specific chemical energy accommodation with finite-rate surface chemistry in non-equilibrium flow

During atmospheric reentry, the vehicle surface is exposed to highly non-equilibrium flow. The vehicle surface can experience heterogeneous recombination of reactive atoms, which contributes to its aerothermodynamic heating. This process is followed by chemical energy accommodation (CEA), where the released energy is either transferred to the surface or the internal energy modes of the recombined molecule. Heterogeneous recombination can be categorized into Eley–Rideal (ER) and Langmuir–Hinshelwood mechanisms, which differ in their methods of molecule formation and degrees of CEA. The complete CEA assumption may not consider the dependency of CEA on the mechanisms of heterogeneous recombination. This study aims to consider the mechanism-specific CEA for a more accurate prediction of surface heat flux. The authors implement mechanism-specific CEA within the direct simulation Monte Carlo framework using the finite-rate surface chemistry model, resolving elementary surface reactions and assigning a CEA coefficient, β, to each mechanism. The model is verified through comparisons with analytical solutions of surface coverage and validated against benchmark references. A parametric investigation of rarefied hypersonic flow over a two-dimensional cylinder is conducted under different freestream Mach and Knudsen numbers. Results show a reduction in total heat flux of up to 14.44% using mechanism-specific CEA compared to the complete CEA assumption. The reduction is attributed to the relative contribution of the ER mechanism, which can be a function of atomic partial pressure at the boundary layer.

Drag and Thermal Reduction of Spiked Hypersonic Vehicle in Thermochemical Nonequilibrium

This study utilizes the in-house parallel direct simulation Monte Carlo–quantum dynamics method to model the aerodynamic flowfield of a spiked reentry vehicle within a rarefied high-altitude atmosphere. Investigating the flight of spiked aircraft under various flight conditions and spike sizes and considering both the real gas effect and the rarefied gas effect, the aerodynamic characteristic of the aircraft is evaluated. Performance evaluation for effectiveness in drag reduction and thermal protection is based on drag and the maximum stagnation heat flux coefficient at the vehicle’s shoulder. Findings indicate that, in the rarefied atmosphere, the distinction between the characteristic shock intensities of spiked and unspiked vehicles is not pronounced, which results in a drag reduction of approximately 5%, accompanied by a more than 100% increase in thermal effect on the vehicle’s shoulder, obviously poor in effectiveness. Subsequently, this study examines the spiked vehicle equipped with a lateral jet, and this augmented approach achieves a marked reduction in the intensity of the shock wave impacting the vehicle’s shoulder with a drag reduction exceeding 10% and attenuates the thermal impact by over 50% in comparison to the implementation of spiking alone, thereby demonstrating superior performance in terms of effectiveness.

Efforts to Improve Knowledge and Skills of Splint Dressing with Simulation and Training Methods in Adolescents of Mandala Bhakti Health Vocational School Surakarta

ABSTRACT A fracture is a condition where a bone is cracked or broken due to trauma or physical impact. The strength and angle of physical exertion, the condition of the bone itself, and the soft tissue around the bone will determine whether the fracture is complete or incomplete. The impact of a fracture can cause bone deformity or disability and even death in the victim if help is not immediately provided, where splinting is one of the first aid measures that must be given to patients who experience a fracture. This community service activity aims to help increase the knowledge and skills of teenagers, especially PMR members, in providing first aid when they find a victim who has suffered a fracture. The method used in this activity uses power point media when providing education, then continues with demonstrations and direct simulations for participants on how to apply splints to patients who have fractures. The results of the activity showed the enthusiasm of the participants in carrying out the splint dressing demonstration as well as an increase in participants' knowledge and skills in carrying out the splint dressing, namely during the pre-test, 25% of their knowledge and skills were good, increasing to 81.25% after the education and post-test were carried out. So it can be concluded that providing health education and demonstrations regarding dressing splints really helps teenagers in increasing their knowledge and skills in dressing splints. Keywords: Skills, Splinting, Training

Magnetohydrodynamic and Aerodynamic Assessment of a 70° Spherecone at Mars and Venus

An electrical conductivity database for continuum flow in a CO2 atmosphere over a 70° spherecone was created using the Data Parallel Line Relaxation Code computational fluid dynamics software to inform development of future magnetohydrodynamic subsystems at Venus and Mars. Sixteen freestream conditions were considered at Mars with atmospheric relative velocities from 5 to 8 km/s and altitudes between 20 and 80 km. Sixteen freestream conditions were considered at Venus with atmospheric relative velocities from 9 to 12 km/s and altitudes between 85 and 115 km. Results indicate that the total electrical conductivity in the flow volume always increases as velocity increases. At low velocities, the electrical conductivity is higher at high altitudes whereas, at high velocities, the electrical conductivity is higher at low altitudes. Three of the 80 km altitude computational fluid dynamics solutions show good agreement with direct simulation Monte Carlo results. In general, computational fluid dynamics predicts thinner shocks, higher electron number density, and similar vibrational temperatures to direct simulation Monte Carlo. The magnetohydrodynamic force was calculated at both Mars and Venus. Results indicate there may not be sufficient control authority to use magnetohydrodynamics as a trajectory control mechanism at Mars without artificially increasing the electrical conductivity of the flow, but there may be appreciable control authority for a drag-modulated aerocapture at Venus.

Kinetic investigation of discharge performance for Xe, Kr, and Ar in a miniature ion thruster using a fast converging PIC-MCC-DSMC model

Abstract The present work develops a full particle-based model that couples the particle-in-cell plus Monte Carlo collision (PIC-MCC) simulation for plasma dynamics and the direct simulation Monte Carlo (DSMC) method for neutral dynamics in a synergistic iterative manner. This new model overcomes the slow convergence issue in the conventional direct coupling approach caused by the disparity of the time scales between the plasma and neutral dynamics. This model is applied to simulate the behavior of xenon (Xe) and its potential alternatives, krypton (Kr) and argon (Ar), in the discharge chamber of a miniature direct current (DC) ion thruster. The results show that a stable discharge is difficult to achieve for Kr and Ar under the operating conditions optimal for Xe. While increasing the discharge voltage can effectively improve the stability of discharge for Kr and Ar, other common strategies such as changing the magnetic field strength, propellant flow rate, and cathode current are not successful. The propellant utilization efficiency and discharge efficiency are affected by both discharge voltage and propellant flow rate. A maximum utilization efficiency and an optimal discharge efficiency are observed for all three propellants, with the values decreasing in the order of Xe, Kr, and Ar. Moreover, the discharge voltage corresponding to the optimal efficiency is inversely proportional to the square root of the propellant mass, indicating that the ion diffusional loss to the wall, rather than the ionization energy, is the dominant factor affecting the discharge performance for alternative propellants in a miniature DC thruster.

Numerical investigations of spatiotemporal dynamics of space-charge limited collisional sheaths

Electrostatic particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) methods are used to compare the plasma dynamics of collisionless with collisional emissive sheaths in partially ionized environments. Space-charge limited emissive sheaths submersed in a plasma with a density of ∼1017 m−3 are examined using a PIC-DSMC solver, CHAOS. Collisionless emissive sheaths with plasma domains sufficiently long (30 and 60 Debye lengths, λD) are subject to strong oscillations due to two-stream electron instability, whereas emissive sheaths in weakly collisional conditions with a short domain (15 λD) exhibit self-spike (sawtooth) oscillations in the plasma field due to the trapped charge-exchange (CEX) ion population within the virtual cathode (VC) region. The two-stream electron instability leads to strong temporal fluctuations in the total emission current, with maximum deviations of 60% and 100% from the time-averaged current for the long plasma domains, whereas CEX collisions cause strong spikes in the emission current if the domain size is short. Our PIC-DSMC simulations show for the first time that the interaction of the two types of instabilities causes the strength of the self-spike to be weakened due to the strong fluctuations caused by the two-stream instability when a sufficiently long computational domain with ion-neutral collisions is employed. By conducting a two-dimensional Fast Fourier Transform (FFT) on the collisional and collisionless sheaths with long domains, we show that the transient evolution of CEX entrapment in the VC increases frequency of sheath oscillations up to two times the ion-acoustic frequencies observed in the collisionless sheath. CEX collisions weaken the VC region and result in a total emission current more than that obtained from the collisionless case for the same domain length. With a more rarefied neutral environment of 1019 m−3 in the plasma sheath, the total emission current increases only 4% in comparison with 14% for one order of magnitude denser environment, within 20 μs. In addition, the spike period is tested with different neutral temperatures and densities. While we do not observe any self-spike in the more rarefied environment, the spike period increased from 5 to 7.5 μs when the neutral temperature is increased from 300 to 2000 K in the denser environment with the simulation time of 20 μs.

Modeling Photodissociation: Quantum Dynamics Simulations of Methanol.

A comprehensive computational study of the gas-phase photodissociation dynamics of methanol is presented. Using a multiconfigurational active space based method (RASSCF) to obtain multidimensional potential energy surfaces (PESs) on-the-fly, direct quantum dynamics simulations were run using the variational multi-configurational Gaussian method (DD-vMCG). Different initial excitation energies were simulated to investigate the dependence of the branching ratios on the electronic state being populated. A detailed mechanistic explanation is provided for the observed differences with respect to the excitation energy. Population of the lowest lying excited state of methanol leads to rapid hydroxyl hydrogen loss as the main dissociation channel. This is rationalized by the strongly dissociative nature of the PES cut along the O-H stretching coordinate, confirmed by the broad feature in the absorption spectrum. In contrast, more energetic excitations lead mainly to C-O bond breaking. Again, analysis of the diabatic surfaces offers a clear explanation in terms of the nature of the electronic states involved and the coupling between them. The type of calculations presented, as well as the subsequent analysis of the results, should be seen as a general workflow for the modeling of photochemical reactions.

BAD-NEUS: Rapidly converging trajectory stratification.

An issue for molecular dynamics simulations is that events of interest often involve timescales that are much longer than the simulation time step, which is set by the fastest timescales of the model. Because of this timescale separation, direct simulation of many events is prohibitively computationally costly. This issue can be overcome by aggregating information from many relatively short simulations that sample segments of trajectories involving events of interest. This is the strategy of Markov state models (MSMs) and related approaches, but such methods suffer from approximation error because the variables defining the states generally do not capture the dynamics fully. By contrast, once converged, the weighted ensemble (WE) method aggregates information from trajectory segments so as to yield unbiased estimates of both thermodynamic and kinetic statistics. Unfortunately, errors decay no faster than unbiased simulation in WE as originally formulated and commonly deployed. Here, we introduce a theoretical framework for describing WE that shows that the introduction of an approximate stationary distribution on top of the stratification, as in nonequilibrium umbrella sampling (NEUS), accelerates convergence. Building on ideas from MSMs and related methods, we generalize the NEUS approach in such a way that the approximation error can be reduced systematically. We show that the improved algorithm can decrease the simulation time required to achieve the desired precision by orders of magnitude.

Learning dislocation dynamics mobility laws from large-scale MD simulations

By dispensing with all the atoms and only focusing on dislocation lines, the computational method of Discrete Dislocation Dynamics (DDD) gains greatly over Molecular Dynamics (MD) in simulation efficiency of metal plasticity. But whereas in MD dislocations follow natural dynamics of atomic motion, DDD must rely on a dislocation mobility function to prescribe how a dislocation line should respond to the driving force exerted on it. However, reflecting our still incomplete understanding of ways in which dislocations move, mobility functions presently employed in DDD simulations entail simplifications and approximations of limited or, worse still, unknown accuracy and applicability. Here we introduce a data-driven approach in which the dislocation mobility function is modeled as a graph neural network (GNN) trained on large-scale MD simulations of crystal plasticity. We apply our proposed approach to predicting plastic strength of body-centered-cubic (BCC) metal tungsten and show that, once implemented in a DDD model, our GNN dislocation mobility function accurately reproduces the challenging tension/compression asymmetry of plastic flow observed both in ground-truth MD simulations and in experiment. Furthermore, subsequently validated by MD simulations, the same function accurately predicts plastic response of tungsten under conditions not previously seen in training. By demonstrating its ability to learn relevant physics of dislocation motion, our DDD+ML approach opens a promising avenue to bringing fidelity of DDD models closer in line with direct MD simulations at a much reduced computational cost.

Polymorph-Specific Solubility Prediction of Urea Using Constant Chemical Potential Molecular Dynamics Simulations.

Molecular dynamics simulations offer a robust approach to understanding the material properties within a system. Solubility is defined as the analytical composition of a saturated solution expressed as a proportion of designated solute in a designated solvent, according to IUPAC. It is a critical property of compounds and holds significance across numerous fields. Various computational techniques have been explored for determining solubility, including methods based on chemical potential determination, enhanced sampling simulation, and direct coexistence simulation, and lately, machine learning-based methods have shown promise. In this investigation, we have utilized Constant Chemical Potential Molecular Dynamics, a method rooted in direct coexistence simulation, to predict the solubility of urea polymorphs in aqueous solution. The primary purpose of using this method is to overcome the limitation of the direct simulation method by maintaining a constant chemical potential for a sufficiently long time. Urea is chosen as a prototypical system for our study, with a particular focus on three of its polymorphs. Our approach effectively discriminates between the polymorphs of urea based on their respective solubility values; polymorph III is found to have the highest solubility, followed by forms IV and I.

Control of Flow and Acoustic Fields Around an Axial Fan Utilizing Plasma Actuators

Abstract Small axial fans, commonly employed for cooling electronic equipment, are frequently housed within narrow ducts, where intense tonal sound with duct resonance can occur, particularly when the blade passing frequency or its harmonic frequency aligns with the duct's resonance frequency. To mitigate resonant sound, this study proposes a flow control using dielectric barrier discharge plasma actuators, which induce a flow along the generation of plasma in air. The control effects on flow field, acoustic radiation, and aerodynamic characteristics are evaluated through direct aeroacoustic simulations and experiments conducted at different flow rates. The computational results reveal that swirling flow occurs in the inflow due to fan rotations at low flow coefficients. This swirling flow is weakened by utilizing plasma actuators, which are arranged to induce flows in the circumferentially reverse direction compared to fan rotations. This control method weakens the resonant sound at low and intermediate flow coefficients, while intensifying it at high flow coefficients, all at the same rotational speed. Moreover, the static pressure coefficient decreases and increases at low and high flow coefficients, respectively, with the latter attributed to an increase in the relative inflow angle induced by the control. Experimental findings demonstrate that the acoustic resonance was reduced by the control at both low and high flow rates, achieved by adjusting the rotational speed to maintain the same flowrate and static pressure rise as in the baseline case.

Phase-field modeling of crack growth under coupled creep-fatigue

Crack growth under coupled creep-fatigue strongly influences service life of metallic components operating at high temperatures. However, there lack numerical models that enable direct simulations of crack growth and plasticity development under coupled creep-fatigue. In this study, a unified phase-field model is developed for simulating crack growth under fatigue, creep, and coupled creep-fatigue. This model is able to reproduce the Paris laws for both brittle and ductile materials in pure fatigue mode, which shows that the degradation rate due to cyclic stress in ductile materials is generally larger than that in brittle materials. Fatigue simulations with different yield strengths demonstrate that plasticity facilitates crack growth in typical ductile materials. High-throughput simulations are performed under coupled creep-fatigue conditions, with varying hold-stress levels and hold-time. By analyzing crack growth rate under different hold-time, a creep-fatigue interaction term is obtained. Simulation results demonstrate that the creep-fatigue interaction is caused by smaller stress gradient and enhanced degradation rate ahead of the crack tips under coupled creep-fatigue, compared to the situation of pure fatigue. This work reveals the origin of different Paris-law exponents in brittle and ductile materials and demonstrates how the interplay between creep and fatigue affects crack growth.

An efficient eigenvalue bounding method: CFL condition revisited

Direct and large-eddy simulations of turbulence are often solved using explicit temporal schemes. However, this imposes very small time-steps because the eigenvalues of the (linearized) dynamical system, re-scaled by the time-step, must lie inside the stability region. In practice, fast and accurate estimations of the spectral radii of both the discrete convective and diffusive terms are therefore needed. This is virtually always done using the so-called CFL condition. On the other hand, the large heterogeneity and complexity of modern supercomputing systems are nowadays hindering the efficient cross-platform portability of CFD codes. In this regard, our leitmotiv reads: relying on a minimal set of (algebraic) kernels is crucial for code portability and maintenance! In this context, this work focuses on the computation of eigenbounds for the above-mentioned convective and diffusive matrices which are needed to determine the time-step à la CFL. To do so, a new inexpensive method, that does not require to re-construct these time-dependent matrices, is proposed and tested. It just relies on a sparse-matrix vector product where only vectors change on time. Hence, both implementation in existing codes and cross-platform portability are straightforward. The effectiveness and robustness of the method are demonstrated for different test cases on both structured Cartesian and unstructured meshes. Finally, the method is combined with a self-adaptive temporal scheme, leading to significantly larger time-steps compared with other more conventional CFL-based approaches.

Mechanic-electric-thermal coupling simulation method of Lamb wave under variable temperature

The propagation mechanism of Lamb waves exhibits more intricate in the variable operational environment of high-speed trains. Simulation methods are widely used to study Lamb wave propagation characteristics due to economic and time constraints. A mechanic-electric-thermal coupling simulation method to study the propagation mechanism of Lamb waves under variable temperatures is proposed in this paper. To accurately simulate the dynamic behavior of Piezoelectric Transducer (PZT) under variable temperature, a nonlinear numerical model of the dynamic parameters (piezoelectric coefficient, dielectric constant) of PZTs has been developed based on the experiment of the temperature influence on Lamb wave. The model emphasizes the nonlinear pattern of change in the key dynamic parameters of the PZT with temperature fluctuations. In addition, a thermal expansion stress model of the PZT-bonding layers-structure is established to reveal the mechanical-thermal coupling mechanism. Based on the COMSOL, a mechanical-electrical-thermal direct coupling simulation model of PZT-bonding layers- structure under variable temperature is established. The simulation results at −40 °C to 80 °C are obtained and compared to the experiment. The results show that the simulation signal is highly consistent with the experimental measurement signal, and the simulation method proposed in this paper has high accuracy.

An improved stochastic weighted particle method for boundary driven flows

The stochastic weighted particle method (SWPM) is a generalization of the Direct Simulation Monte Carlo (DSMC) method where particle weights are variable and dynamic. SWPM is backed by a strong theoretical foundation but has not been critically evaluated for problems of practical interest. A thorough assessment of SWPM for boundary-driven flows reveals significant numerical artifacts near the boundary, notably a diverging heat flux. To correct the boundary heat flux, two modifications to SWPM are proposed: separated grouping and a spatially-dependent weight transfer function. To gauge the relative efficiency of SWPM in comparison to DSMC, a high-Mach-number wheel flow which forms a strong density gradient is also simulated.

Two-level parallel load balancing strategy for accelerating DSMC simulations in near-continuum gases

The Direct Simulation Monte Carlo (DSMC) algorithm is widely employed for simulating rarefied gas flows and is increasingly applied in near-continuum regimes for research and engineering purposes. However, its computational demands, notably load imbalance and extended simulation time, hinder widespread adoption. Addressing these challenges, this paper introduces the Two-Level parallel load balancing strategy. This novel approach combines thread-level and multi-process parallelism to enhance load balancing and reduce simulation time. Key features include a thread-level load-decoupling strategy implemented via OpenMP and a multi-process load balancing mechanism employing distributed memory via MPI. Building upon our previous [Formula: see text] [L. Li, W. Ren and B. Zhang, J. Aeronaut. Astronaut. Aviat. Ser. A 46, 88 (2014)] approach, the load balancing mechanism utilizes Stop At Risk (SAR) criteria for repartitioning with METIS. Additionally, a specialized data transmission mechanism utilizing MPI nonblocking communication minimizes global communication between processes. Validation and evaluation are performed using four hypersonic flow cases around a cylinder and sphere, demonstrating significant improvements. Notably, the proposed strategy achieves [Formula: see text] enhancement over the [Formula: see text] strategy under 512 CPU cores compared to 16 CPU cores, and reduces between-process communication time with [Formula: see text]. These advancements contribute to enhancing the effectiveness of the DSMC algorithm in near-continuum aerodynamic simulations.

Higher-order multi-scale physics-informed neural network (HOMS-PINN) method and its convergence analysis for solving elastic problems of authentic composite materials

The limitations of prohibitive computation and Frequency Principle remain difficult for deep learning methods to effectively resolve multi-scale problems. In this work, a novel higher-order multi-scale physics-informed neural network (HOMS-PINN) framework is developed to compute the elastic problems of authentic composite materials with strongly discontinuous and high-contrast material parameters, which inherits the advantages of higher-order multi-scale method and physics-informed neural network, and halves the computational expense remarkably in comparison with direct PINN simulation. In the numerical framework of HOMS-PINN method, two types of network structures including single neural networks and independent neural networks are designed to mesh-free solve lower-order and higher-order microscopic unit cell (UC) functions, and macroscopic homogenization equations of multi-scale composites, which are then assembled into higher-order multi-scale solutions for multi-scale elastic problems by using automatic differentiation technology. Moreover, transfer learning is introduced to extend HOMS-PINN framework accelerating simulation of multi-scale elastic problems for composite materials with high-contrast mechanical parameters. Furthermore, the error estimate of the proposed HOMS-PINN method is demonstrated under some assumptions. Finally, numerous numerical experiments including high-contrast, multi-inclusion and three-dimensional composites are presented to validate the accuracy and effectiveness of HOMS-PINN method, especially for accurately capturing the sharply oscillatory behaviors in micro-scale. This study offers a robust HOMS-PINN computational framework that enables the simulation and analysis of large-scale mechanical problems of authentic composite materials.

Direct simulation of vortex dynamics of multi-cellular Taylor–Green vortex by pseudo-spectral method

This study investigates the long-time vorticity dynamics of the multi-cellular configurations of the two-dimensional (2D) Taylor–Green vortex (TGV). The pseudo-spectral method is used to solve the incompressible Navier–Stokes equation to analyze the evolution of TGV arrays. The focus is on understanding vortex interactions leading to vortex filamentation and stripping (forward cascade) during primary instability; merger and reconnection (inverse cascade) among the TGV vortical cells subsequently. Here, consideration of multiple cells avoids imposing symmetries at the smallest periodic length scale, and thereby affecting disturbance growth. The initial condition is taken from the analytic solution of the TGV, and Fourier spectral method is employed to track the interactions of the initial doubly-periodic vortices. The full sequence of evolution from one equilibrium state to another for the TGV is not addressed before, as reported here to fill this gap for multiple TGV cells in both directions. By studying various vortical interactions in the ensemble, here we report the enstrophy and energy spectra for different number of TGV cells. This is crucial in understanding the very long-time evolution process, at post-critical Reynolds numbers for the 2D TGV problem in the same physical domain, (0≤(x,y)≤4π) having (4×4) and (6×6) cells. Reported results show the evolution of these vortical cells from original configurations to finally a (1×1) vortical cells — the universal state not demonstrated before.