Unsteady Flow Model Research Articles

Reduced-order modelling of unsteady vortex lattice method

The purpose of this research is to present a new idea of reduced-order modelling of unsteady flows without static correction, which is based on fluid eigenmodes. The new reduced order model is formulated based on a new form of wake vortices without static correction. This technique is expected to perform a reduced-order model similar but faster than the previous techniques. The new method is used to analyse unsteady flows over a three-dimensional wing and comparing with the previous techniques. The performances of the present method are demonstrated with numerical examples. The results show the accuracy of the new reduced-order model of unsteady flow with higher computational efficiency. In conclusion, the new method can be considered as an alternative technique to perform the reduced-order models of unsteady flow.

Ignition process and propellant grains distribution of the two-module charge

The accumulation form of propellant grains has a great effect on the initial chamber pressure wave in the ignition and flame-spreading process of a modular charge. In this process, the grains distribution is determined by the dynamic characteristics of grains after the cartridge is broken. Therefore, a visualized ignition simulation experimental device was designed for the ignition test of the two-module charge with different initial loading positions. A high-speed camera system was used to observe the ignition and flame propagation, the rupture of combustible cartridge cases, and the moving process of the propellant grains. The experimental results show as follows. When the two-module charging position is far from the primer and the spacing between the two modules is increased, the time of flame propagation in the chamber is prolonged. And the cartridge cases are more completely burned and their rupture areas become larger. The propellant grains in the chamber are finally scattered in the axial 195–500 mm area starting from the end face of the primer side. The grains are mainly distributed in the steep-slope accumulation on the right side of the chamber. On the basis of the experiment, a three-dimensional unsteady gas-solid two-phase flow model for the modular charge was established. The dynamic process and distribution of the propellant grains was simulated. The calculation results are basically consistent with the test ones, which validate the rationality of the established model.

Generalization of Thermal and Mass Fluxes for the Flow of Differential Type Fluid with Caputo–Fabrizio Approach of Fractional Derivative

In this research work, generalized thermal and mass transports for the unsteady flow model of an incompressible differential type fluid are considered. The Caputo–Fabrizio fractional derivative is used for the respective generalization of Fourier’s and Fick’s laws. A MHD fluid flow is considered near a flat vertical surface subject to unsteady mechanical, thermal, and mass conditions at boundary. The governing equations of flow model are solved by integral transform, and closed form results for generalized momentum, thermal, and concentration fields are obtained. Generalized thermal and mass fluxes at boundary are quantified in terms of Nusselt and Sherwood numbers, respectively, and presented in tabular form. The significance of the physical parameters over the momentum, thermal, and concentration profiles is characterized by sketching the graphs.

On Thermodynamically Compatible Finite Volume Methods and Path-Conservative ADER Discontinuous Galerkin Schemes for Turbulent Shallow Water Flows

In this paper we propose a new reformulation of the first order hyperbolic model for unsteady turbulent shallow water flows recently proposed in Gavrilyuk et al. (J Comput Phys 366:252–280, 2018). The novelty of the formulation forwarded here is the use of a new evolution variable that guarantees the trace of the discrete Reynolds stress tensor to be always non-negative. The mathematical model is particularly challenging because one important subset of evolution equations is nonconservative and the nonconservative products also act across genuinely nonlinear fields. Therefore, in this paper we first consider a thermodynamically compatible viscous extension of the model that is necessary to define a proper vanishing viscosity limit of the inviscid model and that is absolutely fundamental for the subsequent construction of a thermodynamically compatible numerical scheme. We then introduce two different, but related, families of numerical methods for its solution. The first scheme is a provably thermodynamically compatible semi-discrete finite volume scheme that makes direct use of the Godunov form of the equations and can therefore be called a discrete Godunov formalism. The new method mimics the underlying continuous viscous system exactly at the semi-discrete level and is thus consistent with the conservation of total energy, with the entropy inequality and with the vanishing viscosity limit of the model. The second scheme is a general purpose high order path-conservative ADER discontinuous Galerkin finite element method with a posteriori subcell finite volume limiter that can be applied to the inviscid as well as to the viscous form of the model. Both schemes have in common that they make use of path integrals to define the jump terms at the element interfaces. The different numerical methods are applied to the inviscid system and are compared with each other and with the scheme proposed in Gavrilyuk et al. (2018) on the example of three Riemann problems. Moreover, we make the comparison with a fully resolved solution of the underlying viscous system with small viscosity parameter (vanishing viscosity limit). In all cases an excellent agreement between the different schemes is achieved. We furthermore show numerical convergence rates of ADER-DG schemes up to sixth order in space and time and also present two challenging test problems for the model where we also compare with available experimental data.

Sum-of-delay models for pressure control in Water Distribution Networks

Service pressure control is a powerful tool to reduce leakage and risk of pipe bursts in Water Distribution Networks (WDNs). However, to obtain good control performances, it is essential to rely on a good model of the plant. A typical approach consists of the identification of a linear, local model of the system around the desired working point. Previous works relied on black-box, high order models to demonstrate that WDNs are characterised by a very complex dynamic behaviour, which should be properly modelled to avoid stability issues resulting from poor regulator design. This work aims at providing a physical justification for such complex dynamic behaviour, by means of a particular grey-box model structure, with pure delays as its fundamental blocks. Moreover, this works demonstrates that the new model structure can be very effective and efficient in modelling the WDN dynamics. Finally, to proper exploit the new model, this work proposes a bi-objective optimisation based procedure for the regulator design. The potentialities of both model identification and regulator design phases are assessed by means of simulated experiments performed on a detailed unsteady flow model of three different WDNs.

Computational Fluid Dynamics Study of Cerebral Thromboembolism Risk in Ventricular Assist Device Patients: Effects of Pulsatility and Thrombus Origin.

This study investigates the hypothesis that by surgically manipulating the outflow graft (OG) implantation during ventricle assist device placement, it may be possible to reduce the risk of cerebral embolism. We investigate this hypothesis using a computational approach on a patient-specific basis under fully pulsatile hemodynamics with a multiscale computational fluid dynamics model incorporating a coupled Eulerian-Lagrangian scheme that effectively tracks emboli in the fluid domain. Blood is modeled as a non-Newtonian fluid based on the hematocrit level. Preliminary flow analysis shows that depending on the anastomosis angle the left ventricular assist device (LVAD) can enhance the flow to the cerebral circulation by nearly 31%. Z-test results suggest that unsteady-flow modeling ought to be an integral part of any cardiovascular simulation with residual ventricular function. Assuming unsteady-flow conditions, a shallow LVAD outflow graft anastomosis angle is the most optimal if thrombi are released from the aortic-root reducing cerebral embolization incidence to 15.5% and from the ventricle to 17%, while a more pronounced anastomosis angle becomes advantageous when particles originate from the LVAD with an embolization rate of 16.9%. Overall, computations suggest that a pronounced LVAD anastomosis angle is the better implementation. Unsteady modeling is shown to be necessary for the presence of significant antegrade aortic-root flow which induces cyclical flow patterns due to residual pulsatility. On the other hand, depending on thrombus origin and ventricular assist devices (VAD) anastomosis angle there is a strong tradeoff in embolization rates.

Influence of Varying the Stage Aspect Ratio on the Performance of Multi-Stage Savonius Wind Rotors

Abstract Although using a multi-stage rotor of Savonius vertical-axis wind turbine enhances the self-starting ability, it reduces the power coefficient. To improve power coefficient, the influence of varying the stage aspect ratio is investigated. Therefore, two-, three-, and four-stage Savonius rotors at stage aspect ratios ranging from 0.5 to 1.5 with increments of 0.25 are considered. To determine performance parameters such as coefficients of torque, power, and thrust, a comprehensive three-dimensional unsteady incompressible turbulent flow model using Reynolds-averaged Navier–Stokes (RANS) equations along with a k–ω shear stress transport turbulence model is developed. The developed numerical model is validated utilizing the available experimental results. Moreover, a novel assessment technique relying on flow field characteristics such as pressure distribution in conjunction with streamlines around the proposed multi-stage Savonius rotor with various stage aspect ratios is carried out. The contribution of each stage on the performance of the whole rotor is computed and presented. The findings of the current study illustrate that utilizing a multi-stage rotor with stage aspect ratio equal to or greater than 1.0 significantly enhances the output power. By rising the stage aspect ratio within the range of 0.5–1.5, the peak coefficient of power boosts from 0.163 to 0.213 for a two-stage rotor and from 0.183 to 0.23 for a four-stage rotor. In addition, three-stage rotors with stage aspect ratio ranging from 0.5 to 1.5 show increased average static coefficient of torque from 0.196 to 0.272 with positive values at whole rotation angles. This improves the self-starting abilities of the multi-stage rotor and makes it suitable in areas where the wind is intermittent and very low. Furthermore, raising the stage aspect ratio from 0.5 to 1.5 significantly mitigates the oscillations of both torque and thrust coefficients throughout the entire cycle for all multi-stages. This lowers the mechanical vibrations and noise emission during operation conditions. Accordingly, multi-stage Savonius rotors with stage aspect ratio equal to or greater than 1.0 are highly recommended for practical applications.

Testing of an Optimization-Simulation Model for Real-Time Flood Operation of River-Reservoir Systems

A new methodology was developed for the real-time determination gate control operations of a river-reservoir system to minimize flooding conditions. The methodology is based upon an optimization-simulation model approach interfacing the genetic algorithm within MATLAB with simulation software for short-term rainfall forecasting, rainfall–runoff modeling (HEC-HMS), and a one-dimensional (1D), two-dimensional (2D), and combined 1D and 2D combined unsteady flow models (HEC-RAS). Both real-time rainfall data from next-generation radar (NEXRAD) and gaging stations, and forecasted rainfall are needed to make gate control decisions (reservoir releases) in real-time so that at time t, rainfall is known and rainfall over the future time-period (Δt) to time t + Δt can be forecasted. This new model can be used to manage reservoir release schedules (optimal gate operations) before, during, and after a rainfall event. Through real-time observations and optimal gate controls, downstream water surface elevations are controlled to avoid exceedance of threshold flood levels at target locations throughout a river-reservoir system to minimize the damage. In an example application, an actual river reach with a hypothetical upstream flood control reservoir is modeled in real-time to test the optimization-simulation portion of the overall model.

Evaluation of flood damage reduction throughout Japan from adaptation measures taken under a range of emissions mitigation scenarios

This study aimed to evaluate the impact of climate change on flood damage and the effects of mitigation measures and combinations of multiple adaptation measures in reducing flood damage. The inundation depth was calculated using a two-dimensional unsteady flow model. The flood damage cost was estimated from the unit evaluation value set for each land use and prefectures and the calculated inundation depth distribution. To estimate the flood damage in the near future and the late twenty-first century, five global climate models were used. These models provided daily precipitation, and the change of the extreme precipitation was calculated. In addition to the assessment of the impacts of climate change, certain adaptation measures (land-use control, piloti building, and improvement of flood control level) were discussed, and their effects on flood damage cost reduction were evaluated. In the case of the representative concentration pathway (RCP) 8.5 scenario, the damage cost in the late twenty-first century will increase to 57% of that in the late twentieth century. However, if mitigation measures were to be undertaken according to RCP2.6 standards, the increase of the flood damage cost will stop, and the increase of the flood damage cost will be 28% of that in the late twentieth century. By implementing adaptation measures in combination rather than individually, it is possible to keep the damage cost in the future period even below that in the late twentieth century. By implementing both mitigation and adaptation measures, it is possible to reduce the flood damage cost in the late twenty-first century to 69% of that in the late twentieth century.

A method of determining leaks transported liquid from the pipeline

The problem of detecting leaks of oil and petroleum products from the pipeline is considered. For the mathematical description of the problem we use one-dimensional mathematical model of unsteady flow of a viscous incompressible fluid in pipeline, which includes the equation of motion and equation of continuity of fluid flow. In this case, the liquid leak is represented as a point drain described by the Delta function, and the continuity equation is compiled taking into account the point drain. The pressure and volume flow of the liquid in the initial and final sections of the pipeline are considered set. Taking into account the features of point runoff, the task is split into two tasks with matching conditions. Analytical solutions to the obtained problems are determined and explicit formulas are derived for determining the volume flow rate of the liquid for leakage and the coordinates of the leak location in the pipeline.

Efficient Steady and Unsteady Flow Modeling for Arbitrarily Mis-Staggered Bladerow Under Influence of Inlet Distortion

Abstract Accurate and efficient predictions of the steady and unsteady flow responses due to the blade-to-blade variation as well as due to the nonaxisymmetric inlet distortion have been continually pursued. Computation of two problems concurrently has been rarely done in the past partly because of the need to perform whole annulus bladerow simulations, despite the advances in the current state-of-the-art methods with the phase-shift single passage simulations. The current work attempts to deal with this challenge by developing a new computational approach based on the principle of the multiscale method in the framework of a commercial solver (CFX). The methodology formulation relies on summation of the constituent source terms, each of which corresponds to a particular flow perturbation. The source term element corresponding to the blade-to-blade variation effect is linearly superimposed as in the classical Influence Coefficient Method. The unsteady flow field around a blade at any time instant depends only on its relative position to all its neighboring blades, so that the influences of an arbitrarily mis-staggered bladerow can be computed efficiently. In addition, the source term arisen due to the inlet distortion is calculated based on the spatial Fourier transform. A key enabler is that the source terms can be precomputed using a small set of identical blade passages. The source term is then propagated to different spatial and temporal locations depending on the combination of the mis-staggering pattern and the inlet distortion. The multiscale treatment makes it possible to predict a high-resolution flow field effects on the base coarse mesh as if a fine mesh were locally solved, while achieving a considerable computational efficiency gain. The proposed influence-coefficient and source term based method has been validated for test cases with a uniformly staggered bladerow, and for an arbitrarily mis-staggered bladerow, under a clean inflow condition as well as that subject to an inlet distortion.

Unsteady Approximate Model of Grouting in Fractured Channels Based on Bingham Fluid

It is of great significance for the improvement of grouting technology and engineering practice to master the flow law of grout between parallel plates. However, the traditional calculation model ignores the influence of the inertia term and only considers the stable flow of slurry, so there is a big error in some cases. It is difficult to solve the motion equation of a Bingham fluid considering the inertial force term directly. Combined with the relationship between the steady-state flow equation of a Bingham fluid and a Newtonian fluid, the approximate unsteady-state flow equation of a Bingham fluid suitable for describing slurry flow is constructed. In addition, according to the unsteady flow equation, the relationship between the time and distance of slurry flow in parallel plate fractures can be obtained, and the simplified conditions of the Bingham fluid unsteady flow model are given. Finally, the accuracy of the flow equations and the simplified conditions are verified by experiments and numerical calculations.

Parameter sensitivity and economic analyses of an interchange-fracture enhanced geothermal system

Previous research has shown that interchange-fracture enhanced geothermal systems show desirable heat extraction performance. However, their parameter sensitivity has not been systematically investigated. In this study, a three-dimensional, unsteady flow and heat transfer model for an enhanced geothermal system with an interchange-fracture structure was established. The influences of pivotal parameters, including stimulated reservoir volume permeability, fracture spacing, fracture aperture, and injection flow rate on the thermal extraction performance of the interchange-fracture enhanced geothermal system were systematically researched. In addition, the economics of this system were evaluated. The results show that the heat extraction performance of the interchange-fracture system is significantly affected by a change of stimulated reservoir volume permeability and injection flow rate. Increasing permeability reduces electricity costs and improves economic income, while increasing the injection flow rate increases output power but hinders the long-term running stability of the system. Our research provides guidance for the optimal design of an interchange-fracture enhanced geothermal system. Cited as : Yu, G., Liu, C., Zhang, L., Fang, L. Parameter sensitivity and economic analyses of an interchange-fracture enhanced geothermal system. Advances in Geo-Energy Research, 2021, 5(2): 166-180, doi: 10.46690/ager.2021.02.06

Performance evaluation of a novel vertical axis wind turbine using twisted blades in multi-stage Savonius rotors

To enhance the performance of vertical axis wind turbines, a new configuration using twisted blades in multi-stage Savonius rotors is developed. Accordingly, single-, two-, three-, and four-stage Savonius rotors with twisted blades are investigated and compared with a single-stage rotor at corresponding aspect ratios ranging from 1 to 4. To determine performance parameters such as torque, power, and thrust coefficients, a comprehensive three-dimensional unsteady incompressible turbulent flow model using Reynolds-Averaged Navier-Stokes equations along with k-ω shear-stress transport turbulence model is developed. The developed numerical model is validated using the available numerical and experimental results. Furthermore, a novel assessment technique relying on flow field characteristics such as pressure distribution in conjunction with streamlines around the proposed multi-stage Savonius rotor with twisted blades is carried out. The contribution of each stage on the performance of the whole rotor is also computed and presented. The findings of this study show that the new design of the multi-stage rotor with twisted blades significantly enhances the output power. The maximum power coefficient is found to be 0.253 for a two-stage rotor and reaches 0.261 for a four-stage rotor and about 0.223 for a single-stage rotor. In addition, the multi-stage rotor with twisted blades significantly mitigates the oscillations of both torque and thrust coefficients throughout the whole cycle. This lowers the mechanical vibrations and noise emission during operation conditions. The static torque coefficient is found to have positive values with smooth fluctuations at all rotational angles. This results in enhancing the self-starting capability of the multi-stage rotor with twisted blades and making it suitable in areas where the wind is intermittent and very low. The large benefits offered by the proposed multi-stage Savonius rotor with twisted blades model is comparable to alternate designs of vertical axis wind turbines currently in the market.

Influence of gas transmission network failure on security of supply

This paper investigates the influence of failure of transmission network key elements on security of natural gas delivery. The proposed framework combines the probabilistic structure integrity study and the hydraulic analysis. A factor called a volumetric loss was introduced to quantify the effect of network failure. Based on the magnetic flux leakage diagnostics, the rupture probability of steel tube plastic collapse was estimated using a random variable method and Monte Carlo solution. In-line inspections should monitor only the rate of tube wall corrosion, whereas the proposed methodology enables the pipeline operator to evaluate the system ability to deliver gas at the customer nodes. For the hydraulic analysis, an unsteady gas flow model was applied using conservation principles of mass, momentum, and energy. The flow model was tuned to real pressure and temperature data using a multi-objective optimization approach. To demonstrate the practical value of the methodology, the time and amount of gas shortage, line pack, and a volumetric loss were computed for a real tree-topological pipeline network. Simulations demonstrated that the highest volumetric loss is experienced when both compressor stations are shut down. The aim of the proposed algorithm is identification of critical nodes as well as evaluation of measures for improving the gas supply reliability to the customers.

A one-dimensional flow model enhanced by machine learning for simulation of vocal fold vibration.

A one-dimensional (1D) unsteady and viscous flow model that is derived from the momentum and mass conservation equations is described, and to enhance this physics-based model, a machine learning approach is used to determine the unknown modeling parameters. Specifically, an idealized larynx model is constructed and ten cases of three-dimensional (3D) fluid-structure interaction (FSI) simulations are performed. The flow data are then extracted to train the 1D flow model using a sparse identification approach for nonlinear dynamical systems. As a result of training, we obtain the analytical expressions for the entrance effect and pressure loss in the glottis, which are then incorporated in the flow model to conveniently handle different glottal shapes due to vocal fold vibration. We apply the enhanced 1D flow model in the FSI simulation of both idealized vocal fold geometries and subject-specific anatomical geometries reconstructed from the magnetic resonance imaging images of rabbits' larynges. The 1D flow model is evaluated in both of these setups and shown to have robust performance. Therefore, it provides a fast simulation tool that is superior to the previous 1D models.

Flood Hazard Assessment for the Tori Levee Breach of the Indus River Basin, Pakistan

Levee breaches are some of the most common hazards in the world and cause the loss of lives, livelihoods, and property destruction. During the 2010 flood in Pakistan, the most devastating breach occurred at Tori Levee on the right bank of the Indus River, downstream of the Guddu Barrage, which caused residual floods in northern Sindh and the adjoining regions of the Balochistan province. In this study, 2D unsteady flow modeling performed for Tori Levee breach computed residual flood inundation by coupling a HEC-RAS (Hydrological Engineering Centre—River Analysis System) 2D hydraulic model with remote sensing and Geographic Information System techniques. The model performance was judged by comparing the observed and simulated water levels (stage) during peak flow at seven different gauging stations located within the Indus River reach and daily flood extents and multi-day composites. The quantitative values for the calibration and validation of the HEC-RAS model showed good performance with a range of difference from 0.13 to −0.54 m between the simulated and observed water levels (stage), 84% match for the maximum flood inundation area, and 73.2% for the measure of fit. The overall averages of these values for the daily flood comparison were 57.12 and 75%, respectively. Furthermore, the simulated maximum flow passed through the Tori Levee breach, which was found to be 4994.47 cumecs (about 15% of peak flow) with a head water stage of 71.56 m. By using the simulated flows through the Tori Levee breach, the flood risk maps for the 2010 flood identified hazard zones according to the flood characteristics (depth, velocity, depth times velocity, arrival time, and duration). All the flood risk maps concluded the fact that the active flood plain was uninhabitable under flood conditions.

Calibration of projection-based reduced-order models for unsteady compressible flows

An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-vortex interaction occurs at the trailing edge. Results show that calibration produces stable and long-time accurate Galerkin and LSPG ROMs for both cases investigated. The impact of hyper-reduction is tested on LSPG models via an accelerated greedy missing point estimation (MPE) algorithm. For the first case investigated, LSPG solutions obtained with hyper-reduction show good comparison with those obtained by the full order model. However, for the supersonic case the transient features of the flow need to be properly captured by the sampled points of the accelerated greedy MPE method. Otherwise, the dynamics of the moving shock wave are not fully recovered. The impact of different time-marching schemes is also assessed and, differently than reported in literature, Galerkin models are shown to be more accurate than those computed by LSPG when the non-conservative form of the Navier-Stokes equations is solved. For the supersonic case, the Galerkin and LSPG models (without hyper-reduction) capture the overall dynamics of the detached and oblique shock waves along the airfoil. However, when shock-vortex interaction occurs at the trailing-edge, the Galerkin ROM is able to capture the high-frequency fluctuations from vortex shedding while the LSPG presents a more dissipative solution, not being able to recover the flow dynamics.

Double Solutions and Stability Analysis of Micropolar Hybrid Nanofluid with Thermal Radiation Impact on Unsteady Stagnation Point Flow

The mathematical modeling of unsteady flow of micropolar Cu–Al2O3/water nanofluid driven by a deformable sheet in stagnation region with thermal radiation effect has been explored numerically. To achieve the system of nonlinear ordinary differential equations (ODEs), we have employed some appropriate transformations and solved it numerically using MATLAB software (built-in solver called bvp4c). Influences of relevant parameters on fluid flow and heat transfer characteristic are discussed and presented in graphs. The findings expose that double solutions appear in shrinking sheet case in which eventually contributes to the analysis of stability. The stability analysis therefore confirms that merely the first solution is a stable solution. Addition of nanometer-sized particle (Cu) has been found to significantly strengthen the heat transfer rate of micropolar nanofluid. When the copper nanoparticle volume fraction increased from 0 to 0.01 (1%) in micropolar nanofluid, the heat transfer rate increased roughly to an average of 17.725%. The result also revealed that an upsurge in the unsteady and radiation parameters have been noticed to enhance the local Nusselt number of micropolar hybrid nanofluid. Meanwhile, the occurrence of material parameter conclusively decreases it.

Modeling of unsteady flow around well with hydraulic fracture

At present, hydraulic fracturing technologies are widely used for intensification of oil and gas recovery from reservoirs with hard-to-recover reserves. Modeling the processes of flow through porous reservoirs with hydraulic fractures has beenfairly completely developed in the steady-state flow approximation. Non-stationary processes of pressure distribution are considered as applied to the theory of hydrodynamic well survey methods, in which asymptotically limited intervals of coordinate and time variations are taken into account, i.e., distances of the order of the well radius and time significantly shorter than the characteristic time of the flow through the porous medium. At the same time, in reservoirs with hard-to-recover reserves (low-permeability reservoirs and high-viscosity oils), the duration of unsteady processes of pressure redistribution can be of the same order as the characteristic time of flow through the reservoir. This study presents new analytical solutions to the problem of the redistribution of non-stationary pressure in the vicinity of a well penetrated by a vertical fracture. The scientific novelty of the study lies in the fact that the model used takes into account, first, the fluid compressibility in the fracture and, secondly, the fluid flow not only through the fracture, but also through the porous reservoir. The solutions to the problems are constructed using the Laplace transform technique. In particular cases, the expressions known in literature follow from the solutions obtained. The analytical solutions obtained are analyzed, which makes it possible to determine the main characteristic features of the flow processes of around a porous medium.