Recursive Lattice Research Articles

Hybrid compressible lattice Boltzmann method for supersonic flows with strong discontinuities

Within the framework of the hybrid recursive regularized lattice Boltzmann (HRR-LB) model, we propose a novel hybrid compressible LB method to ensure the conservation of total energy in simulating compressible flows with strong discontinuities. This method integrates a LB solver to handle the mass and momentum conservation equations via collision-streaming steps on standard lattices, while a finite volume method (FVM) is employed for the conservation of the total energy equation. The flux reconstruction in the FVM is achieved through a momentum coupled method (MCM). The interface momentum, crucial for reconstructing the convective fluxes and determining the upwind extrapolation of passive scalar quantities in MCM, is derived from the LB method. The validity and accuracy of the proposed method are evaluated through six test cases: (I) isentropic vortex convection in subsonic and supersonic regimes; (II) non-isothermal acoustic pulse; (III) one-dimensional Riemann problems; (IV) two-dimensional Riemann problem; (V) double Mach reflection of a Mach 10 shock wave; and (VI) shock–vortex interaction. Numerical results demonstrate that this method surpasses the previous HRR-LB model by Guo et al. [“Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows,” Phys. Fluids 32, 126108 (2020)] in terms of accuracy and robustness when dealing with strong shock waves.

Classical spin-liquid behavior in interactionally distorted antiferromagnetic spin systems on the kagome lattice

The influence of an interaction distortion of the antiferromagnetic system on the kagome lattice on its magnetic and thermodynamic properties is investigated in the framework of the antiferromagnetic J1−J2−J3 spin-1/2 Ising system with three different nearest-neighbor antiferromagnetic interactions on the star kagome-like recursive lattice. The exact solution of the model is found and the phase diagram is determined and analyzed. It is shown that, depending on the model parameters, three antiferromagnetic phases can be identified, which are separated from the paramagnetic phase by the second order phase transitions. The magnetic and entropy properties of all ground states of the model are determined. Three different ground states that arise from the paramagnetic phase in the zero-temperature limit are identified. Due to the frustration, each of these ground states is highly macroscopically degenerated with different values of the residual entropy. In addition, since the paramagnetic phase in the vicinity of these ground states also exhibits high degeneracy with the presence of strong correlations, related to the proximity of the second-order phase transitions, these ground states together with their immediate paramagnetic surroundings can be considered as regions with the classical spin-liquid behavior. It is also shown that the typical anomalous (Schottky-type) behavior of the specific heat with the existence of a two-peak (in general multi-peak) structure in its temperature dependence in the vicinity of the highly macroscopically degenerated ground states can be suppressed by the presence of the second-order phase transitions.

Cooling effects of the derived coolant-film layer from partitioned porous injectors for transpiration cooling

This study aims to reveal the cooling benefits of the derived coolant film from partitioned porous injectors for transpiration cooling. The near-wall flow development and the cooling performance are investigated based on various layouts of porous injectors. The numerical investigation is conducted using an in-house recursive regularized thermal lattice Boltzmann method (RR-TLBM). The validated RR-TLBM solver is accelerated by three Tesla V100 graphic processing units (GPUs) for the simulation of incompressible and coupled-domain transpiration cooling at high Reynolds numbers, based on high-resolution grids with 2.65 × 108 nodes. The results indicate that the near-wall flow shows high momentum with the partitioned porous injectors. And the mean velocity increases by more than 23 % with the same coolant consumption per unit blowing area, which contributes to the coolant-film development and cooling uniformity downstream. Moreover, the partitioned porous layout shows the possibilities of coolant reduction as compared to the single continuous porous injector in Case 1. A reduction of 43 % in total coolant consumption with the partitioned porous layout only results in a decrease of 6 % in cooling performance downstream. Additionally, the partitioned coolant injection improves local cooling performance by roughly 22 %, with better cooling homogeneity at the same total coolant consumption. Turbulent fluctuations are weakened in the partitioned coolant injection zones, which contributes to an improvement in cooling evenness. The partitioned porous layout can be an appropriate choice for transpiration cooling systems.

Effectiveness of the recursive-lattice technique in the investigation of magnetic systems with the pyrochlore structure.

A well-defined higher recursive approximation of the pyrochlore lattice is introduced and its relevance and effectiveness for the systematic investigation of magnetic systems with the pyrochlore structure is studied within the classical antiferromagnetic as well as ferromagnetic spin-1/2 Ising model in the presence of the external magnetic field. The exact solution of the model is found with the explicit analytic expression for the free energy per site of the lattice. The magnetization and entropy properties of all ground states of the antiferromagnetic model are determined and compared to those obtained within the lower recursive approximation of the model on the recursive tetrahedral lattice. The exact analysis of the residual entropies of the model on the introduced recursive lattice explicitly shows that the well-known Pauling entropy of the water ice cannot represent the true residual entropy of the antiferromagnetic model on the regular pyrochlore lattice in the zero external magnetic field. The improvement of the value of the critical temperature of the ferromagnetic model obtained within the introduced higher recursive approximation is also discussed. The analysis performed demonstrates the great efficiency of recursive approximations in the investigation of various magnetic systems with the pyrochlore structure, especially for frustrated antiferromagnetic systems.

Spin-liquid behavior in the classical antiferromagnetic [formula omitted] spin system on the square-kagome lattice: Exact analysis within recursive-lattice approach

Magnetic and thermodynamic properties of the antiferromagnetic J1−J2−J3 spin system, i.e., the spin system with three different nearest-neighbor antiferromagnetic interactions, on the square-kagome lattice is investigated in the framework of the corresponding exactly solvable spin-1/2 Ising model on the recursive square-kagome lattice. The phase diagram of the model is found and it is shown that, depending on the model parameters, the model exhibits the existence of three long-range order (antiferromagnetic) phases, which are separated from the paramagnetic phase by the second order phase transitions. It is also shown that, in the zero temperature limit, the paramagnetic phase splits into three different ground states realized on the lines that separate antiferromagnetic ground states of the model. Due to the frustration, all these “paramagnetic” ground states are highly macroscopically degenerated with strict hierarchy of their residual entropies. Moreover, the high macroscopic degeneracy of the paramagnetic phase in the vicinity of these ground states together with the presence of strong correlations (given by the proximity of the second order phase transitions) allow one to consider the paramagnetic ground states as well as their immediate paramagnetic surroundings as regions with the classical spin-liquid behavior. It is also shown that the presence of the second order phase transitions in the vicinity of the paramagnetic ground states suppresses expected anomalous (Schottky-type) behavior of the specific heat related to the rapid entropy changes caused by the frustration.

Anisotropically suppressed frustration in antiferromagnetic systems on the kagome lattice

The influence of the interactionally generated anisotropy on the magnetic as well as thermodynamic properties of geometrically frustrated antiferromagnetic systems is investigated in the framework of the interactionally generated uniaxially-anisotropic antiferromagnetic J1−J2 spin-1/2 Ising model on the kagome lattice within the recursive lattice approximation. The exact solution of the corresponding model on the star kagome-like recursive lattice is found and the phase diagrams of the ground states of the model with and without the presence of the external magnetic field are identified from the magnetization as well as the entropy point of view. The magnetization, the entropy, and the specific heat properties of the model are investigated. It is shown that the presence of even a negligibly small interactionally generated anisotropy can lead not only to the quantitative but also to the significant qualitative changes in the magnetic and thermodynamic properties of frustrated magnetic systems, e.g., it can suppress the presence of frustration itself and, at the same time, generate the appearance of the first and second order phase transitions.

Effective parameter for estimation of efficiency of adiabatic (de)magnetization cooling processes in frustrated magnetic systems

The efficiency of the adiabatic (de)magnetization cooling processes in frustrated magnetic systems is investigated in detail in the framework of an exactly solvable antiferromagnetic model in the presence of the external magnetic field on the recursive kagome lattice. A well-defined parameter is proposed for an effective qualitative as well as quantitative estimation of the efficiency of such cooling processes to the very low temperatures, which takes into account the value of the final temperature as well as the external magnetic field changes needed for the reaching of this temperature. It is shown that the proposed parameter allows one to identify the most effective cooling strategy for given initial conditions.

Single-ion anisotropy as the source of anomalies in thermodynamic properties of magnetic spin-1/2 − 1 mixed systems on square and simple cubic lattices

The influence of the single-ion anisotropy on the thermodynamic properties of ferromagnetic as well as ferrimagnetic spin-1/2 − 1 mixed systems on the square and simple cubic lattice is investigated in the framework of the exactly solvable Ising-like models on the corresponding recursive lattices. The exact solutions of the models are present in the form of the explicit expressions for the free energy per site as the functions of the coordinates of the fixed points of the corresponding systems of recursion relations. The phase diagrams of the models are determined and the existence of compensation temperatures in the ferrimagnetic cases are discussed. The equations that drive the positions of the critical points are derived. The existence of the tricritical behavior in the three-dimensional system on the simple cubic lattice and its nonexistence in the case of the two-dimensional system on the square lattice is demonstrated. It is shown that the presence of the single-ion anisotropy can naturally lead to the emergence of the thermodynamic anomalies typical for frustrated magnetic systems even in unfrustrated ferromagnetic systems on studied bipartite lattices. First of all, the studied models exhibit the formation of strict residual-entropy hierarchies between the neighboring ground states of the system of three different ground states. It is also shown that due to this behavior of the entropy the specific heat capacity of the models exhibit anomalous (Schottky) behavior at low temperatures in the vicinity of the values of the anisotropy parameter, for which highly macroscopically degenerated single-point-like ground states are formed.

Influence of interaction-generated anisotropy on the antiferromagnetic spin system on the octahedral lattice

The phase diagram of the antiferromagnetic spin-1/2 Ising-like model on the octahedral lattice with different strength of the nearest-neighbor interactions in all horizontal planes of the lattice in comparison to all nearest-neighbor interactions between them is investigated in the appropriate recursive lattice approximation. The existence of the intermediate phase that separates two dominant antiferromagnetic phases is shown and the nature of all phase transitions between various phases is determined. The sublattice as well as total magnetization properties of all phases of the model are studied. It is shown that the introduced interaction-generated anisotropy has strong impact on the very existence of the phenomenon of the weak ferromagnetism as well as on its magnetization properties in such pure antiferromagnetic spin systems.

Near-wall vortices and thermal simulation of coupled-domain transpiration cooling by a recursive regularized lattice Boltzmann method

The present study aims to reveal the near-wall vortices and the effects of flow states in coupled-domain transpiration cooling using a recursive regularized thermal lattice Boltzmann method (RR-TLBM). Large-eddy simulations of turbulent flow and heat transfer have been conducted on high-resolution computational grids using a desktop-level computer with CUDA 11.6. Results indicate that the near-wall flow structures present spatial characteristics along the streamwise direction. The vortex evolution promotes the downstream heat dissipation, even though turbulence impairs the effective cooling area. The spanwise evolvement of vortices strengthens the mixing of coolant and hot gas, and small-scale structures are beneficial for turbulent heat transfer. Moreover, the transition onset occurs earlier at higher Reynolds numbers, and it weakens the downstream cooling. The cooling performance of the derived coolant film is improved as the Reynolds number varies from 5 × 103 to 3 × 104 with a blowing ratio of F = 10%, whereas the local cooling is impaired at the high Reynolds numbers exceeding 5 × 104. The variation in flow states has little influence on the cooling performance at the Reynolds numbers larger than 3 × 106. On the other hand, our in-house RR-TLBM solver is highly stable and efficient for the simulation of flow and heat transfer with high Reynolds numbers. Simultaneously, a high computational performance of 1127 million lattices updated per second is achieved for our simulation of a coupled-domain turbulent flow and heat transfer, using the desktop-level computer with three Tesla V100 graphics processing units.

Prediction of the existence of an intermediate phase in the antiferromagnetic J1-J2system on the face-centered cubic lattice

The structure o f the phase diagram of the antiferromagnetic Ising model with the presence of the nearest-neighbor and next-nearest-neighbor interactions on the face-centered cubic lattice is investigated in detail in the framework of the recursive lattice approximation. The existence of an additional well-defined intermediate phase is predicted that separates two standard antiferromagnetic phases of the model. This new phase is realized in the form of a narrow strip in the phase diagram but can be observed for a rather large interval of the frustration parameter of the model. Moreover, analyzing the sublattice magnetization properties of the model, it is shown that transitions between all model phases have the second-order nature. All predicted series of successive phase transitions of the model caused by the presence of the intermediate phase are studied.

Exact calculation of the elastic antiferromagnetic Ising model under static external force on Husimi lattice

We investigate an elastic Ising model with a modified Lennard-Jones potential on the Husimi recursive lattice, where the model can be solved exactly. An external force field to either stretch and press the lattice is applied to approach the elasticity in Ising model in a static way. As expected, both stretching and compressing induce less stability with lower T c, nevertheless due to the asymmetric feature of the LJ well, trivial but realistic destabilization is observed in the stretch case implying the drawing crystallization, and interesting phenomenon of supercooled state and Kauzmann Paradox addressed by zero entropy at finite temperature is observed in the compression case on the left side of the LJ potential well.

Phase diagram and thermodynamic properties of the frustrated ferro-antiferromagnetic spin system on the octahedral lattice

The influence of anisotropy generated by the competition between the ferromagnetic and antiferromagnetic nearest-neighbor interactions on the magnetic and thermodynamic properties of the classical spin system on the octahedral lattice is investigated in the framework of the exactly solvable Ising-like model on the recursive octahedral lattice. The phase diagram of the model is found and the nature of all phase transitions is determined. It is shown that the model exhibits the existence of the intermediate phase that separates the ferromagnetic phase from the antiferromagnetic one. Moreover, it is also shown that while the intermediate phase and the antiferromagnetic one are separated by the critical curve of the second-order phase transitions the transitions between the ferromagnetic phase and the intermediate one have the first-order nature on the coexistence line. The magnetization and entropy properties of all phases of the model are studied. Depending on the value of the frustration parameter, four different ground states are identified with formation of a strict residual entropy hierarchy. Due to the frustration nature of the model the specific heat capacity exhibits anomalous (Schottky) behavior at low temperatures in the vicinity of the value of the frustration parameter, for which two highly macroscopically degenerated single-point-like ground states are formed. The presence of the intermediate phase in the model also leads to the existence of the series of even three successive second-order phase transitions in the temperature dependence of the magnetization as well as of the specific heat capacity.

Wasp-waisted hysteresis in magnetic materials with octahedral structure: A theoretical explanation based on exactly solvable model

The possibility of the existence of two different but thermodynamically equivalent ferromagnetic-like phases below the critical temperature in magnetic materials with octahedral structure is shown in the framework of an exactly solvable model with the competition between nearest-neighbor ferromagnetic and antiferromagnetic interactions on the octahedral recursive lattice. This observation offers a natural base for a fundamental theoretical explanation of the existence of anomalous wasp-waisted-like hysteresis measured in various perovskites with basic octahedral structure. Besides, it is shown that the corresponding ground states are highly macroscopically degenerated. This leads to the presence of frustration effects in the model thermodynamics in their vicinity. In this respect, the anomalous behavior of the specific heat capacity is demonstrated.

Interaction-generated frustration in the ferromagnetic spin system on the kagome lattice: Exact analysis on the star kagomelike recursive lattice.

Frustration effects caused by the presence of the six-site interaction in the ferromagnetic spin-1/2 Ising system on the kagome lattice are investigated in detail using the star kagomelike recursive lattice approximation. It is shown that although the model always exhibits the existence of only two standard phases (the ferromagnetic phase and the paramagnetic one) separated by the curve of the second-order phase transitions, depending on the value of the multisite interaction, the ferromagnetic phase splits into three different ground states in the zero-temperature limit with different magnetization and thermodynamic properties. The free energy of the model is derived, the residual entropies of all ground states are determined, and it is shown that the presence of the six-site multisite interaction leads to the formation of two highly macroscopically degenerated ground states in the studied ferromagnetic system, one of which is realized only for unique ratio of the six-site interaction to the ferromagnetic interaction. It is demonstrated that the existence of this highly macroscopically degenerated single-point-like ground state leads to appearance of the Schottky anomaly in the low-temperature behavior of the specific heat capacity in the vicinity of this ground state. It is also shown that the simultaneous presenceofthe frustration and of the second-order phase transitions in the studied model is responsible for the existence of even three local maxima in the temperature behavior of the specific heat capacity.

Field-induced tricriticality in antiferromagnetic [formula omitted] spin systems on body-centered cubic lattice

The influence of the external magnetic field on the phase diagram of the classical antiferromagnetic spin-1/2 system with the nearest-neighbor and the next-nearest-neighbor antiferromagnetic interactions on the body-centered cubic lattice is investigated in detail using the recursive lattice approximation. In the framework of this exactly solvable model the explicit expression for the free energy per site is found and the nature of all phase transitions is determined. It is shown that applied magnetic field significantly changes the phase diagram of the model. First of all, the presence of arbitrarily weak external magnetic field immediately reduces the number of possible different phases of the model from four to two. Moreover, unlike the case with zero magnetic field, where all phase transitions are of the second-order type, the nature of the phase transitions between these two remaining model phases depends on the values of the parameters of the model. More precisely, the region of the first order phase transitions appears when the external magnetic field is switched on, which is separated from the region of the second order phase transitions by the curve of the tricritical points. It is also shown that such magnetic systems can exhibit series of even three successive phase transitions in the temperature dependence. On the other hand, at most one field-induced phase transition of the first-order or second-order type exists in the field dependence. The sublattice magnetization properties of the model are studied and the magnetization properties of the various types of series of successive phase transitions are demonstrated.

A hybrid recursive regularized lattice Boltzmann model with overset grids for rotating geometries

Simulating rotating geometries in fluid flows for industrial applications remains a challenging task for general fluid solvers and in particular for the lattice Boltzmann method (LBM) due to inherent stability and accuracy problems. This work proposes an original method based on the widely used overset grids (or Chimera grids) while being integrated with a recent and optimized LBM collision operator, the hybrid recursive regularized model (HRR). The overset grids are used to actualize the rotating geometries where both the rotating and fixed meshes exist simultaneously. In the rotating mesh, the fictitious forces generated from its non-inertial rotating reference frame are taken into account by using a second order discrete forcing term. The fixed and rotating grids communicate with each other through the interpolation of the macroscopic variables. Meanwhile, the HRR collision model is selected to enhance the stability and accuracy properties of the LBM simulations by filtering out redundant higher order non-equilibrium tensors. The robustness of the overset HRR algorithm is assessed on different configurations, undergoing mid-to-high Reynolds number flows, and the method successfully demonstrates its robustness while exhibiting the second order accuracy.

Lossless compression of hyperspectral images using recursive least square lattice filter group

Lossless compression of hyperspectral images using recursive least square lattice filter group

Influence of metamagnetic phase transitions on thermodynamics of frustrated systems with octahedral structure

Common effects of the geometric frustration and of the metamagnetic phase transitions on the thermodynamic properties of antiferromagnetic systems with the octahedral structure are investigated using an exactly solvable antiferromagnetic model on the octahedral recursive lattice. The residual entropies of all ground states are determined and the existence of two highly macroscopically generated single-point ground states with nonzero residual entropies is shown. The first-order character of the metamagnetic phase transitions of the model is demonstrated by discontinuous behavior of the entropy. The presence of the anomalous Schottky-type behavior of the specific heat capacity, i.e., the appearance of an additional peak in the low-temperature behavior of the specific heat capacity, in the vicinity of the magnetic field values, for which the highly macroscopically degenerated ground states are formed, is demonstrated and discussed. It is shown that the geometric frustration of the model together with the presence of the metamagnetic phase transitions can lead to more complicated behavior of the specific heat capacity, e.g., they have impact on the number of peaks (local maxima) in its behavior. It is also shown that the magnetocaloric effects related to the metamagnetic phase transitions are much more pronounced than those related to the frustration.

Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows

Based on recent work by Guo et al. [“An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice,” J. Comput. Phys. 418, 109570 (2020)], an improved thermal hybrid recursive regularized lattice Boltzmann model (iHRR-ρ) on a regular lattice is developed for two- and three-dimensional compressible laminar and turbulent flows. To enhance the numerical stability in a broad range of Courant–Friedrichs–Lewy numbers and in under-resolved simulations, a new equilibrium density distribution function is proposed to enlarge its positivity region in the Mach–temperature plane. An embedded hybridizing procedure is introduced in the quasi-symmetry correction terms, which allow for a decoupled treatment of unphysical modes and physical under-resolved turbulent scales on coarse grids. To handle compressible turbulent flows, the under-resolved scales are modeled using the original hybrid recursive regularized collision model given by Jacob et al. [“A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann method-based large eddy simulation,” J. Turbul. 19, 1051–1076 (2018)] equipped with Vreman’s subgrid model for the large-eddy simulation. The validity and accuracy of the present method for laminar and turbulent compressible flows are assessed by considering six test cases: (I) viscous shock wave internal structure, (II) isentropic vortex convection in a supersonic regime, (III) non-isothermal acoustic pulse, (IV) vortex–shock wave interaction, (V) supersonic flow over NACA airfoil at Re = 10 000 and Ma = 1.5, and (VI) compressible Taylor–Green vortex at Ma = 0.29.