Energy Conservation Equations Research Articles

Self-detection of thermal ambient parameters for air-conditioned space by learning operation data and self-prediction of indoor temperature and power consumption

For efficient energy use of air conditioning unit (AC), there is a need to find an optimal control method for operation. To deduce an optimal control algorithm, indoor temperature and power consumption need to be predicted according to given operating conditions. Among the key factors, the thermal ambient parameters such as thermal resistances of the operation sites are most difficult to identify. This study proposed a method for an AC to deduce these parameters for itself by learning operation data obtained from the embedded sensors and autonomously predict indoor temperature and power consumption by solving the transient energy conservation equation incorporating refrigeration cycle simulation. A novel aspect of this study is that the AC can autonomously perceive thermal ambient parameters of its surroundings and utilize these parameters to predict indoor temperature variations and power consumption. These data could be fed back to the control software of the AC in real time. To validate the proposed method, experiments were conducted in model house test facility using a real air-conditioner, and the results were compared with the simulation results. It was confirmed that the time to reach the air temperature setpoint was within 3 min and the power consumption could be predicted within 9 %.

A simplified single-phase depth-averaged model for rock-ice avalanche movement considering ice melting

This paper considers a simplified single-phase depth-averaged model for simulating rock-ice avalanche movement, which incorporates an energy conservation equation to describe the evolution of mass temperature, accounting for the transition from negative to positive values and vice versa. Additionally, this model introduces a saturation parameter that quantifies the impact of pore water pressure on the normal stress of flow materials. To validate the feasibility of the presented model, two laboratory experiments are simulated. Based on the comparison between numerical results and measured data, this study demonstrates that the presented model captures the transformation of rock-ice avalanches from granular flow to debris flow induced by ice melting during movement and the evolution of associated variables including ice volume fraction and temperature. This study further investigates the impact of factors such as fluid viscosity and melting water on rock-ice avalanche movement through simulation. The findings demonstrate that fluid viscosity has an impact on the morphology of rock-ice avalanches and the rate of ice melting. Consequently, this influence directly affects the movement of rock-ice avalanches. In addition, the cohesive force generated by meltwater impedes the progression of low-speed rock-ice avalanches, particularly those with lower water content.

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

PurposeThe steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered.Design/methodology/approachThe partial differential equations for mass, momentum and energy conservation are changed to the system of ordinary differential equations through similarity solution transformations. Solutions, both numerical and asymptotic, to these similarity equations are found in some new ranges of parameters in the governing equations.FindingsThe equations are solved both asymptotically and numerically for a range of the transpiration parameter S and the flow parameter λ given in Mahros et al. (2023), thus greatly extending the range of these previous solutions. Asymptotic solutions for both large and small values of the Prandtl number σ are derived, showing good agreement with additional numerical integrations. It should be noted that in Mahros et al. (2023), only the case when σ=1 was treated. A solution for large λ when S=1 is obtained, showing a different asymptotic form to the case when S>0 in Mahros et al. (2023). Multiple solutions were seen by them for S<0 and the nature of the lower solution branch as S→0 from below is discussed. The question as to whether the lower branch solutions join as λ>0 when S<0 is resolved through obtaining an asymptotic solution λ small.Originality/valueThe accuracy of the solutions has been checked through a detailed comparison between the solutions obtained numerically and analytically, where excellent agreement has been found. This study is important for scientists working in the area of jet flows to become familiar with the flow properties and behaviour of jets.

Solar-driven gasification for syngas production at low temperatures using a rotary hybrid porous media reactor

Solar-based technologies play a crucial role in the energy transition towards a green circular economy. This work investigates the solar-driven steam gasification of carbon char particles at low temperatures using an indirectly irradiated rotary hybrid porous media reactor. The solar concentration system consists of a heliostat and parabolic dish with a focus on the emitter plate located at the bottom of the reactor, allowing allothermal conditions for hydrogen (H2) and syngas production. The hybrid bed is composed of carbon and alumina particles randomly mixed in a 50/50 proportion in mass. Three sets were tested varying rotation speed of the unit, i.e., Set A (0 rpm), Set B (15 rpm), and Set C (20 rpm). Numerical simulations were performed using a one-dimensional model assessing mass, energy and chemical conservation equations, considering a semi-global kinetic scheme, including three homogeneous and four heterogeneous chemical reactions. The optical design configuration of the solar system, in addition to the high heat recirculation enhanced by the rotation of the reactor, allowed maximum temperatures of 662 K (outer surface) and 573 K (reaction chamber). At this low-temperature range, a good agreement between numerical simulations and experiments was achieved, observing a H2/CO ratio of 0.088 (Set B) and 0.163 (Set C), representing a 5.7% and 3.1% deviation, respectively. Numerical results show an increase in the temperature would lead to a higher H2/CO ratio production. Further studies are necessary to assess hydrogen and syngas production under these operating conditions at high temperatures.

Experiment study on adhesion dynamic characteristics of droplet impacting on an inclined heated surface

The behaviors and mechanisms of droplet impact on an inclined heated surface is of great importance. In this work, an experimental platform for the droplets impact on the surfaces with different inclined angles and temperatures was established to study the various impact patterns and dynamics. The impact pattern, sliding distance, lengths at the leading and trailing edge points and maximum spreading factor were studied in detail. The results show that the impact patterns were classified as adhesion, splash, rebound and breakup patterns. In the adhesion pattern, a sliding distance model was developed based on Newton's second law and force analysis that considered the viscous, adhesion and gravitational forces for different angles. Larger angle promotes length of the leading edge point, inhibits length of the trailing edge point. Higher temperature suppresses the length of the trailing edge point by boiling. In addition, a model for the maximum spreading factor of the inclined surface was developed by combining a spreading prediction mode with an energy conservation equation, which incorporates kinetic, surface and dissipation energies. An increase in the normal Weber number suppresses the maximum spreading factor. Temperature has a different effect on the maximum spreading factor depending on the normal Weber number.

An efficient pressure-based multiphase finite volume method for interaction between compressible aerated water and moving bodies

Maritime structures in heavy seas can experience wave impact events with high loads. The loads can lead to structural failure and even loss of life. Wave breaking in said sea states causes air to be entrained in water as aeration cloads, remaining long enough to be transported and to play a role in the impulsive interaction with the structure. A small amount of air in water already forms a highly compressible mixture. Compressibility influences the magnitude of the impact loads.A new cartesian grid method for compressible multiphase flow is introduced to account for water, air and homogeneous mixtures of air and water. The method is designed to predict the hydrodynamic loads on moving bodies engaging with interfaces between fluids having large density ratios. An equation for conservation of energy is omitted by enforcing pressure-density relations. The interface between fluids is transported using a geometric Volume-of-Fluid method. The interface between fluids and structure is taken care of by a cut-cell method. An additional fraction field for the amount of air in water in combination with a new formulation for the multiphase speed of sound prevent overprediction of compressibility by artificial air entrainment.New experimental data of 2D wedge impacts with aerated water, made available as open data, are presented to demonstrate the validity of the numerical method. For low aeration levels, the simulation results in terms of the impact loads on the wedge and the frequencies of pressure waves generated upon impact are in good agreement with the experimental data. Increasing the level of aeration reduces the maximum impact load on the wedge. Reflected density waves lead to secondary loads on the wedge. The intensity of the secondary loads, relative to the primary load of impact, increases with the aeration level while the density wave frequency decreases.

Conservation equations for open-channel flow: effects of bed roughness and secondary currents

AbstractTime-averaged velocity fields in uniform open-channel flows over rough beds may exhibit spatial heterogeneities due to the effects of bed roughness and secondary currents (SCs). The latter typically originate from the turbulence anisotropy and spatial heterogeneity introduced by the solid and mixed corners (i.e., between sidewalls and water surface), but may also appear due to roughness spanwise heterogeneities, e.g., associated with patchy vegetation distributions or streamwise sediment ridges on the channel bed. In this paper, we propose rigorous conservation equations for momentum, kinetic energy and fluid stresses accounting for the contributions of bed roughness and SCs, separately. Particular attention is given to the terms regulating the energy exchanges between roughness-induced and SC-related motions, which are expected to provide information on the physical mechanisms leading to the generation of roughness-induced SCs. The proposed approach is illustrated using a large-eddy simulation of a rough-bed open-channel flow.

Effect of flow behavior index of CMC solutions on heat transfer and fluid flow in a cylindrical can

AbstractThe objective of this study was to investigate the impact of the flow behavior index (n) on heat transfer and fluid flow in carboxymethyl cellulose (CMC) solutions during the thermal process within a cylindrical container. The study employed a numerical model based on the finite element method to solve the governing equations for mass, momentum, and energy conservation. Four different values of n were considered, ranging from 0.25 to 1, representing varying degrees of non‐Newtonian behavior. The results revealed that this index significantly influenced the apparent viscosity of the fluid, subsequently affecting the fluid flow patterns and heat transfer. Specifically, the n = 0.25 fluid exhibited a notably higher Grashof number (GR) and velocity compared to the n = 1 fluid. The average GR for the n = 0.25 fluid was ~2300 times larger than that of the n = 1 fluid, while the average velocity for the n = 0.25 fluid was ~37 times higher. In addition, the study identified the presence of secondary flow in the CMC solution with n = 0.25, which enhanced fluid mixing and heat transfer. Notably, the slowest heating zone for the n = 1 fluid remained fixed at the mid‐height of the can, whereas for the n = 0.25 fluid, it continuously shifted and contracted, ultimately settling at the 10% height from the bottom of the can. These findings underscore the critical importance of considering the non‐Newtonian characteristics of the fluid and convective flow during heat transfer processes in product applications.Practical applicationsThe study investigates the impact of flow behavior indices of the CMC solution on heat transfer and fluid dynamics within cylindrical containers. By examining parameters such as concentration, temperature, and heating duration, the researcher aims to optimize thermal processing for liquid food products containing thickening agents, such as sauces, soups, or dairy items. These findings significantly contribute to ensuring the safety, quality, and nutritional value of diverse liquid food products. Moreover, the study's insights may lead to energy savings and reduced environmental impact by minimizing heating time and temperature during thermal processing. In summary, this research bridges scientific understanding with practical applications, benefiting both consumers and the environment.

A fully developed viscous electrically conducting fluid through infinitely parallel porous plates

AbstractThe current article deals with the steady behavior of a fully developed viscous electrically conducting and compressible Jeffrey fluid via infinitely parallel porous vertical microchannel in the sight of a transverse magnetic field. The fluid flow problem is modeled using Napier–Stokes and energy conservation equations. To analyze the problem, the leading equations are reformulated into dimensionless forms. These dimensionless transformed equations are described by nonlinear‐coupled ordinary differential equations and are eliminated utilizing the shooting method based on the fourth‐order Runge–Kutta technique through the boundary conditions; this represent slip velocity and temperature‐jump situations on the fluid–fence interface. The model equations are numerically solved with MATLAB's built‐in routine “bvp4c.” The behavior of Jeffrey fluid is described through graphs. The significance of model parameters is scrutinized and discussed in detail through graphs. Various significant impacts are examined in these simulations, such as radiation, magnetic field and viscous dissipation. Furthermore, the essential results of this investigation are the effects illustrated graphically and discussed quantitatively concerning various influencing parameters corresponding to the magnetic parameter, interaction parameter, buoyancy parameter, Darcy parameter, wall ambient temperature ratio, and the fluid‐wall relationship. We noticed that both walls are heated, that is, the velocity decreases with a rising Jeffrey parameter.

Two-temperature modeling of lamellar cathode arc

A three-dimensional, two-temperature (2T) model of a lamellar cathode arc is constructed, drawing upon the conservation equations for mass, momentum, electron energy, and heavy particle energy, in addition to Maxwell’s equations. The model aims to elucidate how the physical properties of electrons and heavy particles affect heat transfer and fluid flow in a lamellar cathode arc. This is achieved by solving and comparing the fields of electron temperature, heavy particle temperature, fluid flow, current density, and Lorentz force distribution under varying welding currents. The results show that the guiding effect of the lamellar cathode on current density, the inertial drag effect of moving arc, and the attraction effect of Lorentz force at the lamellar cathode tip primarily govern the distribution of the arc’s physical fields. The guiding effect localizes the current density to the front end of the lamellar cathode, particularly where the discharge gap is minimal. Both the inertial drag effect and the attraction effect of Lorentz force direct arc flow toward its periphery. Under the influence of the aforementioned factors, the physical fields of the lamellar cathode arc undergo expansion and shift counter to the arc’s direction of motion. A reduction in welding current substantially weakens the guiding effect, causing the arc’s physical fields to deviate further in the direction opposite to the arc motion. In comparison with a cylindrical cathode arc, the physical fields of the lamellar cathode arc are markedly expanded, leading to a reduction in current density, electron temperature, heavy particle temperature, cathode jet flow velocity, and Lorentz force.

Functional and financial analysis of an inclined step solar desalination using phase change nanomaterials.

Recent decades have seen a shortage of water, which has led scientists to concentrate on solar desalination technologies. The present study examines the solar water desalination system with inclined steps, while considering various phase change materials (PCMs). The findings suggest that the incorporation of PCM generally enhances the productivity of the solar desalination system. Additionally, the combination of nanoparticles has been used to PCM, which is a popular technique utilized nowadays to improve the efficiency of these systems. The current investigation involves the transient modeling of a solar water desalination system, utilizing energy conservation equations. The equations were solved using the Runge-Kutta technique of the ODE23s order. The temperatures of the salt water, the absorbent plate of the glass cover, and the PCM were calculated at each time. Without a phase changer, the rate at which fresh water is produced is around 5.15 kg/m2·h. The corresponding mass flow rates of paraffin, n-PCM I, n-PCM III, n-PCM II, and stearic acid are 22.9, 28.9, 5.9, 11.9, and 73 kg/m2·h. PCMs, with the exception of stearic acid, exhibit similar energy efficiency up to an ambient temperature of around 29°. However, at temperatures over 29°, n-PCM II outperforms other PCM.

Dark energy nature of logarithmic f(R,Lm)-gravity models with observational constraints

This work explores the dark energy nature of logarithmic [Formula: see text]-gravity models with observational constraints, where [Formula: see text] represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian [Formula: see text], a flat FLRW space–time metric and an arbitrary function [Formula: see text], where [Formula: see text] is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between [Formula: see text], [Formula: see text] and [Formula: see text]. Using the most recent two observational datasets as 32 [Formula: see text] and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with [Formula: see text] errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term [Formula: see text]. We found that the effective equation of state parameter is in the range [Formula: see text] over [Formula: see text] with present value [Formula: see text].

Sensitivity analysis of MHD nanofluid flow in a composite permeable square enclosure with the corrugated wall using Response surface methodology-central composite design

This work aims to conduct a numerical study on the magnetohydrodynamic (MHD) natural convection of nanofluid within a porous cavity corrugated hot and cold walls. The system comprises an external magnetic field. The study employs a finite element approach to solve the governing equations for momentum and energy conservation, while systematically varying influential parameters such as the Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), and the magnetic parameter (M). The fluctuations in these parameters allow for the analysis of their effects on the Nusselt number, flow patterns and thermal performance. A notable innovation of this research lies in the incorporation of a Response Surface Methodology (RSM)-based sensitivity analysis. This approach yields valuable insights for optimizing thermal management and enhancing energy efficiency in advanced Magnetohydrodynamics (MHD) systems. According to conclusive data, employing a permeable partition instead of a solid partition leads to a notable enhancement in the mean Nusselt value. Specifically, at Ra = 100, the improvement is recorded at 26.28%. Furthermore, at Ra = 104, this enhancement reaches its peak, with a substantial increase of 56.5%.

Computational investigation of the effect of geometry and fuel composition on the performance of a solid oxide fuel cell

The need to reduce the consumption of fossil fuels due to their negative impact on the quality of the air and on the greenhouse effect is causing major changes in the energy sector, with a progressively greater contribution of renewable energy sources to satisfy the global energy demand. Fuel cell technology is emerging as a key player in the energy transition since fuel cells convert directly chemical energy to electricity and heat without pollutant emissions. Among the different types available, solid oxide fuel cells (SOFC) can operate at high temperatures (up to 1000ºC), leading to high efficiency and stability. This work is concerned with the computational investigation of a planar solid oxide fuel cell. The governing conservation equations for mass, momentum, energy, species transport and electric charge are solved for a three-dimensional planar fuel cell. Different fuel and oxidizer compositions are considered and their influence on the performance of the fuel cell is investigated. The results show that when the hydrogen molar fraction in the fuel decreases, the maximum power and temperature decrease. The power, the efficiency and the maximum temperature are greater when the oxidizer is oxygen rather than air. The influence of the geometry of the air and fuel channels is also assessed, namely the dimensions of the channels and the effect of steps and obstacles in those channels.

A first‐order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non‐linear solid dynamics

SummaryThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

Mathematical Simulation for MHD Casson Convective Nanofluid Flow Induced by 3D Permeable Sheet with Chemical Effect

Objectives: Current manuscript focuses on examination of chemical reaction and heat generation impacts on 3D MHD non-Newtonian nanofluid flow with convective boundary conditions induced by permeable sheet. Additionally, Brownian motion, non-Newtonian heating and thermophoretic processes as used for this study. Methods: A computational programme, MATLAB has been used for solving the system of O.D.Es with the help of ODE45 solver. The Runge Kutta Fehlberg approach is implemented to calculate the answer to the expression for temperature, velocity, and nanoparticle concentration after the shooting process. Findings: For a variety of fluid parameters, the temperature, concentration of nanoparticles, and dimensionless velocities are shown and examined, including permeability parameter , magnetic , stretching ratio parameter , Lewis number , Brownian motion and Prandtl number , thermal Biot number , Casson fluid parameter , chemical reaction parameter . The temperature is found to increase with an enhance in the thermal Biot number and to reduce with a greater Prandtl number and stretching ratio parameter. Novelty: Although the immense significance and frequent use of nanofluids in industries and technology, no effort has been made to explore the chemical influence on MHD Casson fluid flow using a three-dimensional permeable sheet. Through similarity transformations, the Runge-Kutta Fehlberg technique converts mass, momentum, and energy conservation equations into ODEs and incorporates boundary conditions. Skin friction and the heat transmission rate past an extending surface, which have an impact on technology and production, can be predicted using the results of this study. Keywords: Chemical reaction, Buongiorno's model, Nanofluid, Biot numbers, 3D permeable sheet

Study on drainage consolidation characteristics and pore-pressure reversal control of water-rich loess under the combined action of electroosmosis–vacuum

The phenomenon of “pore pressure reversal” occurs in the later stage of electroosmosis–vacuum combined drainage of water-rich loess, which causes the mutual interference of water flow directions in the later stage of the drainage process. Based on the theory of porous media and unsaturated soil mechanics, this study establishes a mathematical model for the coupling of the electric, pore pressure, and displacement fields in the drainage consolidation process of water-rich loess under the combined action of electroosmosis and vacuum. The conservation equations of energy, momentum, and mass are coupled under a solid-liquid-gas three-phase system, considering nonlinear variations of parameters, such as electrical permeability coefficients, electrical conductivity, and hydraulic permeability coefficients. Subsequently, the drainage consolidation process of water-rich loess under different electroosmosis and vacuum combination methods is simulated using finite element software. Moreover, applying vacuum loads in a graded manner and conducting electroosmosis at a later stage of the loading procedure can effectively delay the generation of the “pore pressure reversal” phenomenon and the formation of silt layers.

SIMPLIFIED MATHEMATICAL MODEL OF THERMAL RESPONSE IN ABDOMEN AFTER ABDOMINOPLASTY

The search for beauty and perfection brings with it an increase in the number of plastic surgeries. Thus, there is a need for effective postoperative approaches and immediate observation of possible complications, which can lead to more efficient procedures. Among the plastic surgeries, the aforementioned study selected the abdominoplasty surgery as a reference and a certain area 12 x 12 cm, assuming a size in the infra umbilical region, which will supposedly be in the process of tissue repair and with possible temperature changes on the skin surface. The creation of a simplified 2D mathematical modeling to predict the thermal response of the abdomen is presented here. The model considers the local metabolic activities of a healthy skin before the surgical intervention and after it, considering an obstruction of blood flow at a certain point. The model considers such changes by applying mass and energy conservation equations where the amount of O2 supplied regulates the local temperature. Therefore, the reduction of oxygen supplied to the tissues causes a drop in the local temperature representing poor circulation. Decreased local temperature can cause tissue death. Determining the period of low metabolism can be crucial for choosing a treatment and avoiding complications, financial expenses and suffering.

A dynamic mathematical model used for controller design of a supercritical once-through boiler-turbine unit in all load conditions

Recently, widespread adoption of renewable energy significantly impacts the security and stability of power grid. Utilizing coal-fired units in real-time load figuration remains a primary method to ensure grid stability. Therefore, supercritical Once-Through Boiler-Turbine (OTBT) units continuously enhance flexibility to meet the evolving needs of the grid. To broaden the load boundary and achieve fully automated control from unit start-up to rated load, establishing a dynamic mathematical model used for controller design of OTBT units in all load conditions is a necessary prerequisite. This model should accurately predict model outputs in both once-through mode (OTM) and recirculation mode (RCM) while also reflecting the dynamic transition processes between modes. In this study, we first conducted a detailed analysis of the characteristics of recirculation system. Mass and energy conservation equations are established separately for economizer-waterwall system and superheater system, including a level model for storage tank in RCM. Subsequently, through reasonable assumptions and analysis of the transition process, the modified steam dryness is identified as a crucial indicator to distinguish between RCM and OTM. This approach unified the model structures in RCM and OTM, avoiding issues related to model switching during mode transitions. Following this, model parameters were identified based on an improved dynamic search fireworks algorithm. Finally, multiple sets of comparative simulation experiments demonstrated that the established model exhibits high accuracy throughout the unit operation. Results from open-loop simulations indicated that this model can serve as a foundation for controller design of coordinated control system in all load conditions.

Conserved energy–momentum tensor for real-time lattice simulations

We derive an expression for the energy–momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric procedure for the time discretization. In the case of the momentum conservation equation, we obtain an expression that is of higher accuracy in lattice spacing (O(a2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(a^2)$$\\end{document}) than the naive discretization where fields in the continuum expressions are replaced by discretized counterparts. The improvements are verified by performing numerical tests on the derived expressions using classical real-time lattice gauge theory simulations. We demonstrate substantial reductions in relative error of one to several orders of magnitude compared to a naive discretization for both energy and momentum conservation equations. We expect our formulation to have applications in the area of pre-equilibrium dynamics in ultrarelativistic heavy ion collisions, in particular for the extraction of transport coefficients such as shear viscosity.