Transfer Equation Research Articles

Ancient ceramics restoration method based on image processing texture stitching

This study addresses the issue of the existence of a considerable number of ancient ceramic fragments within the gene pool of ancient ceramics in Jingdezhen, as well as the limited efficacy of manual restoration techniques. To this end, an ancient ceramic restoration method based on the stitching of ancient ceramic textures through image processing is proposed. By employing the optimal single responsiveness matrix and state transfer equation, coupled with a random sampling strategy to ascertain the precise matching points and a consistency checking mechanism to preclude erroneous matching, the optimal single responsiveness matrix is devised to meticulously transform and stitch ancient ceramic textures. The dynamic programming idea is employed to identify the optimal stitching path, thereby enhancing the quality of the stitching and facilitating the precise, seamless, and natural integration of the ancient ceramic texture. The average peak signal-to-noise ratio of the stitched image of ancient ceramics is 58.7554, and the mean square error is 0.0866, which demonstrates the efficacy of image processing technology in the restoration of ancient ceramics and facilitates the intelligent advancement of cultural protection.

The role of the hot porous layer in the gas flow in the inner coma

The objective of this work is to study the influence of a highly non-isothermal porous dust layer on the formation of a comet's inner coma. We studied the water gas activity of comet 67P/Churyumov-Gerasimenko to find a link between the gas properties around the comet and the properties of the dust surface crust. The effects on the radiative transfer spectral lines were studied and compared with MIRO remote sensing observations. For cases of spherical and complex nucleus shapes, we validated surface boundary conditions for gas flow obtained from the two-layer consistent thermophysical model. This model accurately estimates the properties of the sublimation products as the gas diffuses through the layer. The gas expansion was then modeled using a 3D parallel implementation of a direct simulation Monte Carlo algorithm. A multi-beam linear interpolation was used to extract the gas density, velocity, and temperature profiles along a given line of sight. Finally, the radiative transfer equation was used to calculate the brightness temperature of the water vapor. The presence of a porous layer results in an increase in gas temperature and a decrease in gas density at the surface. The gas has a greater acceleration due to the higher initial temperature and increased conversion of translational energy to kinetic energy. This reduces the difference in density between the different models, with the densest gas being the coolest, and increases the terminal expansion velocity of the hotter gas. While the gas density differences are small at large distances, the observable water absorption lines are significantly affected. The presence of a porous layer has a large effect on the properties of the gas in the coma, which can be seen by comparing the spectral lines. This demonstrates the potential interest of the approach in improving surface activity models and placing physical constraints on the dust layer.

Construction and verification of distributed hydrothermal coupling model in the source area of the Yangtze River

Study regionThe source area of the Yangtze River, a typical catchment in the cryosphere on the Tibet Plateau, was used to develop and validate a distributed hydrothermal coupling model. Study focusClimate change has caused significant changes in hydrological processes in the cryosphere, and related research has become hot topic. The source area of the Yangtze River (SAYR) is a key catchment for studies of hydrological processes in the cryosphere, which contains widespread glacier, snow, and permafrost. However, the current hydrological modeling of the SAYR rarely depicts the process of glacier/snow and permafrost runoff from the perspective of coupled water and heat transfer, resulting in distortion of simulations of hydrological processes. Therefore, we developed a distributed hydrothermal coupling model, namely WEP-SAYR, based on the WEP-L (Water and energy transfer process in large river basins) model by introducing modules for glacier and snow melt and permafrost freezing and thawing. New hydrological insights for the regionIn the WEP-SAYR model, the soil hydrothermal transfer equations were improved, and a freezing point equation for permafrost was introduced. In addition, the glacier and snow meltwater processes were described using the temperature index model. Compared to previously applied models, the WEP-SAYR portrays in more detail glacier/snow melting, dynamic changes in permafrost water and heat coupling, and runoff dynamics, with physically meaningful and easily accessible model parameters. The model can describe the soil temperature and moisture changes in soil layers at different depths from 0 to 140cm. Moreover, the model has a good accuracy in simulating the daily/monthly runoff and evaporation. The Nash-Sutcliffe efficiency exceeded 0.75, and the relative error was controlled within ±20%. The results showed that the WEP-SAYR model balances the efficiency of hydrological simulation in large scale catchments and the accurate portrayal of the cryosphere elements, which provides a reference for hydrological analysis of other catchments in the cryosphere.

Influence of Phytoplankton on Ocean Albedo

Using numerical methods for solving the radiation transfer equation, ocean albedo values were calculated for a set of bio-op tical characteristics corresponding to situations with different chlorophyll concentrations (1 μg/L and 10 μg/L) and the case of intense coccolithophore bloom (8–12 million cells/L). Calculations were carried out in the spectral range of 280–2800 nm for cases of cloudless sky at various wind speeds and atmospheric transmission. It has been shown that for Case 1 waters, a change in chlorophyll concentration from 1 to 10 μg/L does not lead to changes in albedo. In the case of intense coccolithophore blooms, the ocean albedo can increase more than threefold. Calculation of average monthly albedo values for selected points in the Barents and Black seas showed that the presence of intense coccolithophore blooms significantly increases average monthly albedo values. The calculation of the values of radiation absorbed in the seawater column depending on the time of day, carried out for these points, demonstrated that the presence of blooms significantly reduces the values of absorbed radiation. It is shown that the contribution to the albedo of radiation emerging from water used in the state-of-the-art NEMO numerical ocean model, amounting to 0.005 ± ± 0.0005, corresponds only to Case 1 waters. Intense coccolithophore blooms can increase this contribution by more than 14 times. A simple formula is proposed for correcting albedo values taking into account the influence of bio-optical characteristics.

Modeling the Influence of Raleigh Numbers on Thermal and Fluidic Behaviors in a Trapezoid-shaped Cell

We model the influence of Raleigh numbers in a trapezoidal cavity. One wall among the sloping walls is exposed to a heat flux density Q=100 W/ m<sup>2 </sup>and the other inclined wall is kept adiabatic. The temperature of the two horizontal walls is assumed to be constant such that T<sub>sup</sub>=305K is greater than T<sub>inf</sub>=300K. The equations of heat and mass transfer which direct our template are described by the Navier-Stockes equation. These equations are discretized using the finite difference method and solved by the Thomas and Gauss-Seidel algorithms. Thus, we analyze the effects of the Raleigh numbers (<i>Ra</i>) on temperature profiles T = 303.15 K and speeds v = 0 m/s. For a variation of <i>Ra</i>=10<sup>3</sup>-10<sup>5</sup>, we note that the convective exchanges of the confined air and the different walls become preponderant with the increase in the Rayleigh number. Also, we contact that the speed of the confined air remains high along the horizontal walls for a <i>Ra</i> high number, but low near the inclined walls. These results show the effects of natural convection in this trapezoidal cavity.

Optimizing thermal management with micropolar hybrid nanofluids in spatially dependent magnetic fields

Vortices play a pivotal role in fluid dynamics by enhancing fluid mixing and mass transport, making them crucial for numerous applications. Hybrid nanofluids, combining two types of nanoparticles, offer superior thermal conductivity and heat transfer compared to conventional nanofluids. This study examines the influence of localized magnetic fields on vortex dynamics in a micropolar hybrid nanofluid flow within a vertically oriented cavity, driven by moving horizontal lids along the +ve axis. Magnetic field strips are applied horizontally and vertically to control flow behavior. Using MATLAB-based algorithms and the finite difference method, we solve the governing equations of flow and heat transfer. Key parameters, including magnetic field strength, nanoparticle volume fraction, and Reynolds number, are analyzed for their effects on flow structures and temperature profiles. Results indicate that the magnetic field reduces microrotation and enhances laminar flow, influencing stress distribution and temperature gradients. These insights are valuable for optimizing microfluidic devices, heat exchangers, and drug delivery systems, where control over flow dynamics and temperature is essential.

A robust 3D finite element framework for monolithically coupled thermo-hydro-mechanical analysis of fracture growth with frictional contact in porous media

This paper presents the formulation of a robust integrated framework for the coupled multiphysics and multiple fracture growth analysis in porous media. The finite element-based thermo-hydro-mechanical method for fracture growth with frictional contact (THMf-g) simultaneously solves monolithically coupled equations, incorporating contact and frictional constraints from fracture sliding. It also implements an adaptive process to update fields and geometries during fracture growth, effectively modeling emerging new surfaces. The thermo-hydro-mechanical fields are derived from fundamental principles of mass, momentum, and energy conservation and discretized numerically using the finite element method. Fractures are represented as sub-dimensional surfaces embedded within the volume of the porous medium. The growth of multiple fracture is modeled based on stress intensity factors at fracture tips, with fracture aperture and permeability emerging as dynamic properties of the system. The main novelty of this work lies in extending the implicitly solved monolithic coupling to include frictional and growth modeling for multiple non-planar fractures of emerging geometry in three dimensions. This includes the direct incorporation of cubic terms in the fracture flow equations and convection terms in the heat transfer equations, adopting an incremental method to solve these coupled, nonlinear equations. To ensure energy conservation, the heat equations are resolved using an implicit scheme, establishing a velocity dependency on pressure fields and introducing quadratic terms into the heat equation. Furthermore, the heat transfer equation has been revised to account for the work done on the fluid, enhancing the accuracy of thermal modeling. A contact mechanics leader–follower strategy tracks a conformal mesh split at each fracture, accounting explicitly for permeability changes during deformation and growth, effectively reducing computational complexity and cost. The iterative process for applying these constraints and the solution of the coupled THMf-g with friction and growth is described. The method does not require calibrated material properties or artificial length scale parameters, and relies on laboratory-measured properties with direct physical interpretation. A detailed algorithm is presented, including the updating of apertures and handling of new surfaces during the simulation, accounting for the variability of fracture permeability and its interplay with contact and friction during the non-linear solution. Several validating numerical experiments are benchmarked against analytical solutions, demonstrating the accuracy and reliability of the proposed framework in capturing complex fracture behavior and multiphysics interactions in porous media.

Subsweep: Extensions to the sweep method for radiative transfer

We introduce the radiative transfer postprocessing code Subsweep . The code is based on the method of transport sweeps, in which the exact solution to the scattering-less radiative transfer equation is computed in a single pass through the entire computational grid. The radiative transfer module is coupled to radiation chemistry, and chemical compositions as well as temperatures of the cells are evolved according to photon fluxes computed during radiative transfer. Subsweep extends the method of transport sweeps by incorporating sub-timesteps in a hierarchy of partial sweeps of the grid. This alleviates the need for a low, global timestep and as a result Subsweep is able to drastically reduce the amount of computation required for accurate integration of the coupled radiation chemistry equations. We succesfully apply the code to a number of physical tests such as the expansion of HII regions, the formation of shadows behind dense objects, and its behavior in the presence of periodic boundary conditions.

Heat transfer from a cylindrical heater to a medium with variable thermophysical characteristics and heat source power

The formulation and solution of the problem of non-stationary thermal conductivity in a composite material with variable thermophysical characteristics are considered. Density, heat capacity, thermal conductivity, as well as the power of the heat source due to the hydration reactions of the binder components change during the concrete hardening process. The heat transfer problem is formulated for the general case when there are no calculation formulas for thermophysical transfer coefficients. The “microprocess method” was used to calculate the dynamics of the temperature field. According to this method, the space from the outer surface of the heater is modeled by a system of successively located “rings”. When moving from the previous “ring” to the next one, the charge in the transfer coefficients and the power of the volumetric heat source were taken into account. At the same time, the initial and boundary conditions were corrected. The boundary value problems are formulated in the form of a differential equation of non-stationary heat transfer with an arbitrary initial distribution of transfer potentials, Dirichlet boundary conditions, and a heat source in the form Po=f(Fo).The obtained solutions are analyzed for some particular cases. Prospects for further theoretical and experimental research are determined.

Modeling of the Nanofiltration Process Based on Convective Diffusion Theory

The article formulates the state of the problem of improving the theoretical calculation of the nanofiltration kinetic characteristics in the time cycle of separation of industrial solutions containing copper(II), iron(III), trisodium phosphate and OP-10 (a wetting agent used in electroplating, a product of treating a mixture of mono- and dialkylphenols with ethylene oxide) using the equations of convective diffusion, hydrodynamics and mass transfer. To calculate the kinetic characteristics of the nanofiltration process, the mathematical model was improved by numerically solving the equations of convective diffusion, the Navier–Stokes equation and the flow continuity equation in a polar coordinate system with initial and boundary conditions. The theoretical results obtained in the process of an analytical solution of the system of equations allow calculating changes in concentrations in the permeate and retentate tracts and the permeate volume during nanofiltration separation. The acceptability of the developed nanofiltration method for separating solutions is assessed by comparing the calculated data according to the mathematical model with the experimental data obtained on the nanofiltration unit during separation of solutions containing copper(II), iron(III), trisodium phosphate and OP-10.

Two-dimensional P1 approximation (P1-2D) for the Description of the Radiant Field on Cylindrical Solar Photocatalytic Reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in polar coordinates with the P1 approximation approach (P1-2D) for the description of the radiant field in cylindrical solar photocatalytic reactors. A general expression of the LVRPA was formulated that can be employed on cylindrical photocatalytic reactors with an incident radiation constant along the reactor length. CPC and tubular photocatalytic reactors were used as reactor models and Lambert's cosine law (irradiance) was considered when using the boundary conditions. Simulations were carried out using the commercial TiO2-P25, its optical properties taken from the literature. The LVRPA was found to decrease exponentially from the reactor wall to its center. literature rate of photon absorption per unit of reactor length (VRPA/H) increased exponentially with the catalyst loading until a value where no significant increase was observed and was found to increase with reactor radius, information that agrees with the literature. The optimum catalyst loading with the CPC reactor was about 0.364 g/L with a reactor radius equal to 1.65 cm similar to that found in the literature when using the six-flux model in two dimensions (SFM-2D). The apparent optical thickness τ_App1 newly formulated with the P1 approximation was introduced for optimization purposes and was found more reliable than the optical thickness τ. This parameter not only removes the dependence of the optimum catalyst loading on the reactor's radius but also its dependence on catalyst albedo. τ_App1 was found about 9.73 and 14.6 for CPC and tubular reactors respectively and provides the optimum catalyst loading and the reactor radius that optimize the radiation absorption inside both reactors.

Analysis of Bioheat Transfer with Thermoelastic Effect

The development of thermal therapy always requires more reasonable temperature distribution predictions. Controlling the amount of heating is a common practice within general thermal therapy operations. This paper used a modified three-phase lag (TPL) bioheat transfer equation to describe the behavior of heat conduction in tissue with thermoelastic effect. To explore the effect of thermal load, the tissue was subjected to a constant surface temperature and a pulsed surface heat flux, respectively. The modified TPL bioheat transfer equation involves mixed derivative terms and higher-order time derivatives of temperature. In analyzing such problems, there are mathematical difficulties. Therefore, the hybrid numerical scheme based on the Laplace transform and an improved discrete method was proposed to solve the present problem. The influence of thermoelastic parameters on the behavior of heat transfer in tissue has been investigated. The results depict the effect of thermal load on thermal response within heat transfer medium is obvious. The thermoelastic effect excites the thermal response oscillation, which is intensified for the reduction of material constant characteristic [Formula: see text] and phase lag [Formula: see text], in the heat conduction medium.

Estimation of thermal emission from mixture of CO2 and H2O gases and fly-ash particles

Abstract In the present work the thermal emission from gases and particle mixture is studied comprehensively. The mixture consist of CO2 and H2Ogases along with fly-ash particles and their spectral radiative properties are obtained from HITEMP database and Mie theory, respectively. The Line-by-line method, known for high accuracy is used to estimate radiative heat transfer from gases and particle mixture. Three distinct cases, i.e, pure absorption/emission, pure scattering, and their combined effects are investigated. The spectral radiative transfer equation is solved by finite angle method (FAM) and the correctness of the results is ensured by principle of energy conservation. The anisotropic scattering is modeled using the Henyey-Greenstein method. The influence of radiative properties of the participating medium, along with wall and cavity temperatures, on heat transfer and emission spectrum is evaluated. The radiative heat transfer enhances with introduction of the particles in the gaseous mixture. For pure scattering medium, the emission spectrum on each wall differs and also varies from the emission spectrum of the emitting wall. The particle influence grows notably with higher volume fractions in gaseous mixture. While there is a notable contribution of anisotropic scattering in a purely scattering medium, its significance diminishes in an absorbing, emitting, and scattering medium.

МЕТОД МОНТЕ-КАРЛО ДЛЯ РАСЧЕТА ХАРАКТЕРИСТИК СВЕТОВЫХ ПОЛЕЙ В МОРСКОЙ ВОДЕ

The development of numerical methods for solving the integro-differential radiation transfer equation remains a relevant task. Among them, we can highlight the Monte Carlo method, which is in demand in various niches of modern ocean optics. The purpose of this work is a clear and concise presentation of the basics of the forward Monte Carlo method of light fields modeling in seawater, accompanied by a detailed description of its software implementation. The basics of the method are described, the procedures for choosing the type of interaction, the mean free path and the direction of photon motion are described. A simple case is considered, corresponding to an infinitely distant point source of unpolarized light, the absence of atmospheric influence, a smooth air-seawater interface, and the absence of stratification of inherent optical properties. In this case, realistic values of the absorption and scattering coefficients were used, calculated in accordance with the Case 1 model for a chlorophyll concentration of 1 μg/L, and a strongly elongated Henyey-Greenstein phase function with the parameter g = 0.95. The Fresnel reflection of light from the air-seawater interface was taken into account. The relative errors in the values of the diffuse attenuation coefficient for downward irradiance K d and the diffuse reflectance R, calculated in the spectral range of 400–700 nm using 106 photons, in comparison with the HydroLight results were 1.5 % and 0.4 %, respectively. Spectral calculation on one core of a 2017 Intel Core i5-8250U mobile processor in MATLAB takes 6 minutes. An assessment of the choice of the optimal number of photons required to obtain the desired quantities with a given accuracy was made. The implemented method is useful for becoming familiar with the basic principles used to numerically solve the radiative transfer equation in seawater using statistical methods and is used in the “Ocean Optics” course, taught by the author to 4th year students of the Department of Thermohydromechanics of the Ocean at MIPT.

Comparative numerical study of the energy performance of two different configurations of a hybrid photovoltaic/thermal air collector

Solar energy is a renewable alternative to fossil fuels. When solar energy is converted into electricity by photovoltaic (PV) solar modules, the heat generated increases the temperature of the PV solar cells and, as a result, reduces their electrical efficiency. Several techniques are used to cool PV solar cells in order to reduce their operating temperature. One technique is the use of hybrid photovoltaic/thermal (PVT) solar collectors, which simultaneously produce electricity and useful heat. In the airflow channel, the heat and mass transfer equations and those derived from the energy balance on the solid layers of the collector were discretized using the finite difference method with an implicit alternating directions (ADI) scheme. All the algebraic equations obtained after discretization were solved using the Thomas algorithm. The aim is to make a numerical comparison of the energy performance of the Verre-PV-Tedlar and Verre-PV-Verre flat-plate air PVT hybrid solar collectors in the climatic conditions of Lomé, Togo. Under the same operating conditions, the average electrical efficiencies of the Verre-PV-Verre and Verre-PV-Tedlar flat-plate air PVT hybrid collectors are 15.34% and 13.85% respectively. There is a 1.49% improvement in electrical efficiency for a Verre-PV-Verre air-source PVT hybrid collector compared with a Verre-PV-Tedlar PVT hybrid collector. The Verre-PV-Verre flat plate PVT air hybrid collector has an average daily electrical energy gain of 0.564 kWh and a thermal energy gain of 0.839 kWh, while the Verre-PV-Tedlar flat plate PVT air hybrid collector has an average daily electrical energy gain of 0.548 kWh and a thermal energy gain of 1.403 kWh.

Thermal Evaluation of Solar Dryer’s Curve-Front utilized Heat Transfer Analysis

The sun is most sustainable renewable energy, environmentally friendly and utilized for preservation of food and agricultural crops. The main objective of this experiment research work has focused on using renewable energy for evaporated moisture of foods fruit vegetables and herbs by drying system. The heat transfer equation are analyzed to effectively harness the temperature from the sun. Experimental data obtained were used to evaluate the properties of dry air on boundary region condition. Initial, testing was carried out under without load condition, and the result shows that the ambient and dryer’s internal temperature range between 29.3-40.2˚C and 37.4-60.3 ˚C, respectively, in Thailand a latitude of 14°0'48.46" North and longitude of 100°31'49.76" East (recorded average solar radiations and temperature on January 2023 - June 2024), average solar radiations range between 312 W/m2 and 513 W/m2. The indirect natural convection was design and calculated energy base on average temperature not higher than 55˚C, utilized sun daylight at 08:00 a.m. to 04:00 p.m. local time and clear sky or partially cloudy. Second, determination of design parameters; heat energy equation and steam table analysis. Final, utilization of the design under local time, solar radiation and the climatic local conditions and test with ginger slices (represent product in order to examine weight loss). The solar dryer’s curve front shape conduced on without load showed the heat transfer coefficient natural convections range between 3.7 and 4.5 W/m2 ˚C, the energy of dry air analysis range between 54.7 and 155.2 J/s and performance of drying rate range between 0.06 and 0.82 g/s, under increasing and decreasing trends of solar radiations from the time, date and climatic local region condition.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Physics-informed neural networks for modeling atmospheric radiative transfer

Understanding the radiative transfer processes in the Earth’s atmosphere is crucial for accurate climate modeling and climate change predictions. These processes are governed by complex physical phenomena, which can be generally modeled by the radiative transfer equation (RTE). Solutions to the RTE are obtained by various methods including numerical (standard RTE solvers), stochastic (Monte-Carlo), and data-driven (machine-learning) approaches. This paper introduces a novel numerical approach utilizing a Physics-Informed Neural Network (PINN) to solve the RTE in atmospheric scenarios, applying physics constraints in a machine-learning framework. We show that our PINN model offers a flexible and efficient solution, enabling the simulation of radiance values using plane-parallel atmosphere, and under diverse conditions, including clouds and aerosols.

Initial-Boundary Value Problems for the Moisture Transfer Equation with Different Order Fractional Derivatives and Nonlocal Linear Source

Initial-Boundary Value Problems for the Moisture Transfer Equation with Different Order Fractional Derivatives and Nonlocal Linear Source

An implicit unified gas-kinetic particle method with large time steps for gray radiation transport

For a long time, efficient algorithms for high-dimensional equations, represented by photon radiation transport, have been one important topic in the development of computational methods for particle transport processes. In this paper, we present an implicit unified gas-kinetic particle (IUGKP) method for multiscale gray radiative transfer. Based on the integral solution of the radiative transfer equation, the photon transport processes are categorized into non-equilibrium transport processes with a large photon free path and equilibrium transport processes with a small photon free path. The long-path processes are solved by an implicit Monte Carlo (IMC) method, and the short-path processes are solved by an implicit diffusion system. The closure formulation of photon distribution is derived from the local integral solution of the radiative transfer equation to couple the IMC and diffusion system. The improvement of the proposed IUGKP method over UGKP method is that particles can be tracked continuously instead of just until the first collision, making simulation with large time steps possible. The IUGKP method has the properties of asymptotic-preserving (AP) and regime-adaptive (RA). The AP property states that the IUGKP method converges to the consistent numerical methods for the asymptotic limiting equations of RTE in the limiting regimes. The RA property states that the computational accuracy of the IUGKP method adapts to the regimes. In this paper, the mathematical proof of the AP and RA properties is presented, and the multiscale numerical tests are performed to demonstrate the accuracy and efficiency of the IUGKP method.