Hydrodynamic Problem Research Articles

Fluctuating hydrodynamics of an autophoretic particle near a permeable interface

We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields can be expressed in terms of integrals. The resulting boundary-domain integral equations provide a direct way of obtaining the traction on the particle, requiring the solution of linear integral equations. An exact solution for the chemical and hydrodynamic problems is obtained for a particle in an unbounded domain. For motion near boundaries, we provide corrections to the unbounded solutions in terms of chemical and hydrodynamic Green's functions, preserving the dissipative nature of autophoresis in a viscous fluid for all physical configurations. Using this, we give the fully stochastic update equations for the Brownian trajectory of an autophoretic particle in a complex environment. First, we analyse the Brownian dynamics of particles capable of complex motion in the bulk. We then introduce a chemically permeable planar surface of two immiscible liquids in the vicinity of the particle and provide explicit solutions to the chemo-hydrodynamics of this system. Finally, we study the case of an isotropically phoretic particle hovering above an interface as a function of interfacial solute permeability and viscosity contrast.

Machine Learning Visualization Tool for Exploring Parameterized Hydrodynamics

Abstract We are interested in the computational study of shock hydrodynamics, i.e. problems involving compressible solids, liquids, and gases that undergo large deformation. These problems are dynamic and nonlinear and can exhibit complex instabilities. Due to advances in high performance computing it is possible to parameterize a hydrodynamic problem and perform a computational study yielding Ο(TB) of simulation state data. We present an interactive machine learning tool that can be used to compress, browse, and interpolate these large simulation datasets. This tool allows computational scientists and researchers to quickly visualize "what-if" situations, perform sensitivity analyses, and optimize complex hydrodynamic experiments.

From kinetic flocking model of Cucker–Smale type to self-organized hydrodynamic model

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker–Smale model with a confining potential in a mesoscopic scale to the macroscopic limit system for self-propelled individuals, which is derived formally by Aceves-Sánchez et al. in 2019. In the traditional kinetic equation with collisions, for example, Boltzmann-type equations, the key properties that connect the kinetic and fluid regimes are: the linearized collision operator (linearized collision operator around the equilibrium), denoted by [Formula: see text], is symmetric, and has a nontrivial null space (its elements are called collision invariants) which include all the fluid information, i.e. the dimension of Ker([Formula: see text]) is equal to the number of fluid variables. Furthermore, the moments of the collision invariants with the kinetic equations give the macroscopic equations. The new feature and difficulty of the corresponding problem considered in this paper is: the linearized operator [Formula: see text] is not symmetric, i.e. [Formula: see text], where [Formula: see text] is the dual of [Formula: see text]. Moreover, the collision invariants lies in Ker([Formula: see text]), which is called generalized collision invariants (GCI). This is fundamentally different with classical Boltzmann-type equations. This is a common feature of many collective motions of self-propelled particles with alignment in living systems, or many active particle system. Another difficulty (also common for active system) is involved by the normalization of the direction vector, which is highly nonlinear. In this paper, using Cucker–Smale model as an example, we develop systematically a GCI-based expansion method, and micro–macro decomposition on the dual space, to justify the limits to the macroscopic system, a non-Euler-type hyperbolic system. We believe our method has wide applications in the collective motions and active particle systems.

Wave energy extraction from rigid rectangular compound floating plates

We present a theoretical model to analyse the hydrodynamics of wave energy converters (WECs) comprised of three-dimensional, rigid, floating, compound rectangular plates in the open sea. The hydrodynamic problem is solved by means of Green’s theorem and a free-surface Green’s function. Plate motion is predicted through decomposition into rigid natural modes. We first analyse the case of a single rectangular plate and validate our model against experimental results from physical model tests undertaken in the COAST laboratory at the University of Plymouth. Then we extend our theory to complex shapes and arrays of plates and examine how the geometry, incident wave direction and power take-off (PTO) coefficient affect the response of the platform and the consequent absorbed energy.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.

Development of Reduced-Order-Discrete-Module method for hydroelastic analysis of floating flexible structures

The present study proposes a novel method for analyzing the hydroelastic response of floating flexible structures based on Reduced-Order-Discrete-Module (RODM) model. In this model, the floating flexible structure is discretized into a finite number of modules. The hydrodynamic problem is simplified as the interaction between waves and multiple modules. The hydroelastic response is approximated by solving the motion equation of the multibody system, in which the mass and stiffness of the structure are obtained from the reduced-order matrices by the finite element method with a system equivalent reduction expansion process. By using the transformation matrix, the detailed floating structure response can be reconstructed from the multibody dynamics. The validity of the proposed method was demonstrated by comparing the results with the experimental data and other existing methods. The results show that this study has developed an accurate hydroelastic model to analyze the hydroelastic response of floating flexible structures. A module number selection formula is proposed to select the appropriate number of modules based on the exciting force frequency. This model is relatively easy to implement for the hydroelastic problem of interconnection modules and take into account the spatial inhomogeneity of wind/wave field. The proposed model can offer a useful tool for analyzing the hydroelastic response of the offshore floating photovoltaic systems.

An efficient flux-reconstructed lattice boltzmann flux solver for flow interaction of multi-structure with curved boundary

Recently, the escalating computational capability provided by advanced GPU technology for numerical simulations is well-suited for tackling large-scale engineering challenges. The lattice Boltzmann flux solver (LBFS), as a relatively new fluid-solving method, combines the parallelization characteristics of the lattice Boltzmann method (LBM) with the ability to handle non-uniform grids. Building upon these advantages, this study aligns its flux computational steps with the demands of the GPU parallel computing environment, thus developing an efficient flux-reconstructed lattice Boltzmann flux solver (FRLBFS), the improved algorithm not only ensures precision but also achieves a significant enhancement in efficiency, reaching up to a remarkable 500-fold improvement. Additionally, this work combines the immersed boundary method, significantly improving the efficiency of addressing hydrodynamic problems with multiple structures. Through numerical validation, under identical GPU hardware conditions, the proposed method in this paper outperform LBM in terms of computational efficiency. Lastly, simulations of flow past an array of eight cylinders at different Reynolds numbers are conducted, instantaneous contour plots at various dimensionless time points and time-dependent curves of drag and lift coefficients for different cylinders are provided, to demonstrate the complex vortex shedding surrounding multiple cylinders and its extraordinary computational efficiency.

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

A comparative study on aquatic environment of two mega reservoirs in the mainstream of Yangtze River

With the mega dams being built in large rivers around the world for water resources utilization and flood prevention, their environmental impacts such as algae bloom are increasingly concerned by the professionals and the publics, but the mechanism controlling the occurrence of algae are still unclear. Along the mainstream of the Yangtze River, world-class reservoirs have been put into operation successively. Among these reservoirs, the Three Gorges Reservoir (TGR) and the cascade reservoirs (CRs) are adjacent but the conditions of algae bloom in the tributary bays of them are totally different. To explore the reasons of the distinguished situations and factors relating to the high frequent algae bloom in the tributary bays of the TGR, a comparative study was carried out between the TGR and its neighbored reservoir out of the CRs based on field survey investigation, water quality records and literature review. The result reveals the considerable influences of geological and climatic factors on the hydrodynamic processes and environmental problems happening in the tributary bays of mega reservoirs. The two reservoirs exhibit significant differences in physical properties such as the hydrodynamic condition, terrain characteristics and climate. The field-investigation suggests that the water columns in the tributary bays of the CRs tend to experience weak vertical stratification. The analysis shows that this is the result of the combining result of the local terrain characteristics and the cooler, rainier and cloudier climate in the CRs region which significantly affect the hydro-thermal dynamic processes in the tributary bays. With the low level of nutrient and strong vertical mixing, the growth of the algae is constrained and these should be the significant reasons of the low frequency of algae bloom in the tributary bays of the CRs.

Wave-Current Interaction Effects on the OC4 DeepCwind Semi-Submersible Floating Offshore Wind Turbine

In order to investigate the hydrodynamic performances of semi-submersible type floating offshore wind turbines (FOWTs), particularly the effect of body-wave-current interaction, the OC4 FOWT is considered in the presence of co-existing regular wave and uniform current fields. The wind loads are not considered at this stage. The problem is treated in the framework of potential-flow theory in the frequency domain, assuming waves of small steepness, and the solution is obtained by using a perturbation expansion method for the diffraction potential with respect to the normalized current speed. Analytical and numerical formulations have been used to treat the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for the derivation of the associated perturbation potential. The hydrodynamic loads were obtained after evaluating the pressure field around the multi-body configuration using three different computer codes. The results from the three computer codes compare very well with each other and with the numerical predictions of other investigators. Finally, the mean second-order drift forces are calculated by superposing their zero-current values with the corresponding current-dependent first-order corrections, with the latter being evaluated using a ‘heuristic’ approach.

A new frequency domain method to solve the potential flow problem

The potential flow theory is a reliable tool widely-used in ocean engineering to solve the fluid hydrodynamic problems such as the wave hydrodynamic problems. The Rankine source and its image about the seabed is often chosen as the Green's function to solve the potential flow problems for its simple form, easy singular-integral treatment and few boundary conditions in the boundary integral equations. However, traditionally, the boundary element method based on it is only executed in the time domain by time stepping technique which requires lots of computation due to the time domain form of the damping zone's boundary condition. To apply this Green's function in frequency domain, this paper derived a parameterized frequency-domain formula for the boundary condition of the damping zone, and successfully applied the Rankine source and its image about the seabed in frequency domain. This paper's work possesses a great potential to promote the efficiency in solving the potential flow problems.

High order conservative finite difference WENO scheme for three-temperature radiation hydrodynamics

The three-temperature (3-T) radiation hydrodynamics (RH) equations play an important role in the high-energy-density-physics fields, such as astrophysics and inertial confinement fusion (ICF). It describes the interaction between radiation and high-energy-density plasmas including electron and ion in the assumption that radiation, electron and ion are in their own equilibrium state, which means they can be characterized by their own temperatures. The 3-T RH system consists of the density, momentum and three internal energy (electron, ion and radiation) equations. In this paper, we propose a high order conservative finite difference weighted essentially non-oscillatory (WENO) scheme solving one-dimensional (1D) and two-dimensional (2D) 3-T RH equations respectively. Following our previous paper [7], we introduce the three new energy variables, and then design a finite difference scheme with both the conservative property and arbitrary high order accuracy. Based on the WENO interpolation and the strong stability preserving (SSP) high order time discretizations, taken as an example, we design a class of fifth order conservative finite difference schemes in space and third order in time. Compared with the Lagrangian method we proposed in [7], which can only reach second order accuracy for 2D 3-T RH equations if straight-line edged meshes are used, the finite difference scheme can be easily designed to arbitrary high order accuracy for multi-dimensional 3-T RH equations. The finite difference formulation is also much less expensive in multi-dimensions than finite volume schemes used in [7]. Furthermore, our method can handle fluids with large deformation easily. Numerous 1D and 2D numerical examples are presented to verify the desired properties of the high order finite difference WENO schemes such as high order accuracy, non-oscillation, conservation and adaptation to severely distorted single-material radiation hydrodynamics problems.

A hybrid modeling approach: dynamic simulation of two-phase fluid flow in compacting gas condensate reservoirs using potential flow theory

Simulating the flow processes of complex hydrocarbon mixtures, such as gas condensate mixtures and volatile oils, in deep reservoirs is one of the most challenging problems in reservoir hydrodynamics. The challenge lies in meeting three requirements simultaneously when creating a simulator: high accuracy, low computational cost, and high reliability. These metrics determine the performance of the simulation. Meeting all these requirements at the same time necessitates a hybrid approach to solving the problem and optimizing the computational algorithm in terms of CPU time. A new technique has been developed for hybrid modeling of the development of deposits of complex hydrocarbon mixtures. This technique integrates the theory of potential flow, the Binary Flow Model (which accounts for rock compaction, PVT properties of reservoir fluids, phase transformation, and mass transfer between phases), and the material balance equations of the hydrocarbon system using time discretization. In this case, to linearize nonlinear differential equations for the flow of a gascondensate mixture, the method of averaging reservoir pressure along the radial coordinate was used. By introducing the Khrestianovich function, an algorithm was obtained to determine the rate of inflow of the gas-condensate mixture to the well. Using material balance equations for gas and condensate, it was possible to obtain differential equations that describe changes in reservoir pressure and condensate saturation over time. Based on this technique, a simulator for a gas condensate reservoir was created, enabling computer studies to be conducted. The results demonstrated the proposed technique's good accuracy compared with the results of the semi-analytical solution. Keywords: dynamic modeling; simulation; monitoring; streamline; hybrid modeling; binary model.

A Poisson-bracket scheme for nonlinear shallow-water sloshing in an oscillating tank with irregular bottom surface

The mass-, energy-, and potential-enstrophy-conserving Poisson bracket numerical scheme introduced by Arakawa & Lamb (1981), and extended by Salmon (2004) and Stewart & Dellar (2016), is adapted to the problem of nonlinear shallow-water sloshing over a variable bottom surface in a rigid rectangular basin undergoing a prescribed coupled surge-sway motion. Adaptation to a finite domain requires a new approach to the boundary conditions at solid boundaries in the context of the Arakawa C grid. In this paper, the boundary condition at the vertical walls is taken to be vanishing of the normal derivative of the tangential velocity. This gives zero potential vorticity at the boundary, and is consistent with the material conservation of the potential vorticity. This condition, coupled to symmetric boundary conditions for the wave height arising from a reduced version of the evolution equations at boundaries, leads to an extension of the class of staggered C-grid Poisson-bracket schemes to interior flows with solid boundaries. The scheme is implemented, shown to preserve Casimirs, and applied to a range of problems in shallow water hydrodynamics including interaction of travelling hydraulic jumps at resonance, and X-type soliton interactions over a variable bottom surface. This structure-preserving scheme provides a robust building block for long-time simulation of floating ocean wave energy extractors.

Investigation on algorithms for simulating large deformation and impact loads

It is a challenge to simulate the hydrodynamic problems covering the large deformation of the free surface arising in severe circumstances with intense flow. This paper investigates algorithms based on the moving particle semi-implicit method for simulating large deformation and impact loads. The algorithm discretizes the fluid domain into a series of particles, each representing a part of the fluid. The pressure field calculation is implicit, and the velocity field calculation is explicit. Three models, including the gradient model, source term, and free-surface detection, have been improved and compared to determine which improvement is the best to enhance the accuracy and stability. The enhanced pressure gradient guarantees that momentum conservation can be satisfied. Particle density and velocity divergence are incompressible conditions combined in the mixed source term approach. The arc approach is used in the free-surface judging process. The results show that the combination of three models is the most effective in exploring the problems of hydrodynamic pressure and dam break. The issue of liquid sloshing including roll and sway investigates the effect of the initial distance and time step. It is found that the simulation accuracy of impact pressure can be increased as the initial distance and the time step decrease. Finally, the free surface breaking and liquid splashing phenomena are easily observed, and the method can accurately simulate the massive deformation of the free surface. These findings are helpful for hazard assessments of the various fluid mechanics-related problems.

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10−3 to 10−1, which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

Thermocapillary migration of a compound drop in an arbitrary viscous flow

The thermocapillary migration of a concentric compound drop in an arbitrary viscous flow under the consideration of negligible Reynolds number is investigated. The thermocapillary effect refers to the migration of a drop under the influence of a temperature gradient. The thermal and hydrodynamic problems are examined. The thermal field is governed by the heat conduction equation whereas the hydrodynamic fluid velocities are governed by the linearized Navier–Stokes equations. Presence of temperature gradient results in variation of the interfacial tension which is assumed to depend on temperature linearly. Variation of interfacial gradient leads to the coupling of the hydrodynamic problem with the thermal problem through the boundary condition. A complete general solution of Stokes equations is utilized to obtain closed-form expressions for the velocity vector and pressure. The hydrodynamic forces acting on the compound drop are obtained and expressed in terms of Fax́en’s law. Some important asymptotic limiting cases of hydrodynamic drag are also derived. The hydrodynamic drag for cases of uniform flow, shear flow, and heat source with the known ambient flow are derived and it is found that in the case of shear flow, the hydrodynamic drag is contributed only by the thermal component and the shear flow has no effect on it. The obtained results for drag and torque in the limiting cases are in agreement with the existing results in the literature. Furthermore, the migration velocity of the compound drop is obtained by equating the hydrodynamic drag force to zero. The results obtained for migration velocity are explained with the aid of graphs. The migration velocity is found to be a monotonic function of the Marangoni number and the radius of the innermost drop.

Development of the discrete vortex method in combination with the fast multipole method in hydrodynamic problems

In this paper, the flow of a non-viscous incompressible fluid is discussed in terms of vorticity. In the framework of the discrete vortex method, each material particle of the fluid is considered in Lagrange variables; in this case, the velocities are determined by the Biot-Savard law. Thus, the influence of vortices on each other is taken into account. The aim of the work is to construct a numerical method of different orders of accuracy in the problems of vortex dynamics. The fast multipole method used in combination with the standard midpoint and fourth order Runge-Kutta methods significantly reduces the algorithmic complexity. In the fast multipole method, any vortex system is represented by discrete vortices. The fluid domain, determined by the motion of vortices, is divided into several ring-type subdomains, in each of which the velocities are calculated sequentially. To verify the combinability of the numerical methods, three test cases are considered: the dynamics of the symmetric and asymmetric Lamb-Chaplygin dipoles, as well as the rotation of the fluid occupying a cylindrical region of finite radius. It is known that the latter example is rather complex for direct numerical calculations in contrast to the elementary representation of its analytical solution. In fact, the performed calculations confirm that, without the Fast Multipole Method, the numerical treatment for this test case is hardly possible at a sufficiently large number of discrete vortices within a reasonable amount of time. The results of the test calculations are presented in the form of graphs and tables. The application of the standard discrete vortex methods combined with the fast multipole method shows that, due to the optimal number of subdomains and discrete vortices, the time of calculations can be significantly reduced.

Numerical Simulation of Ship-added Resistance Based on a Numerical Wave Tank

The wave resistance increase of a ship during its actual voyage can affect its speed and safety. To design ships with excellent sailing performance, it is necessary to accurately predict the wave resistance increase of a ship in waves, as well as the motion response and wave resistance prediction of ships in waves, which involves complex hydrodynamic problems. This paper first establishes a physical model of the KCS vessel, then utilizes the numerical wave tank platform independently developed by our university. Based on viscous flow theory, it calculates the resistance of the KCS under calm water conditions. Using three-dimensional potential flow methods and spectral analysis, it computes the wave-induced resistance values for the KCS under six-degree sea states, analyzes the wave-induced resistance performance of the KCS, and ultimately, based on the calculation results of calm water resistance and wave-induced resistance combined with propeller efficiency parameters, calculates the effective power of the engine.

A New Approach to the Use of Non-Primitive Variables in the Mechanics of Continuous Media

The problem of an approximate solution to hydrodynamic problems is the consideration of pressure. To exclude it from the equations, the transition to “non-primitive variables” (vortex and velocity vector divergence) is made. In this case, there are difficulties in the algorithmization of new equations for solving the inverse problem of hydrodynamics and a lot of internal iterative calculations. The object of this study includes equations in “non-primitive” variables. The research methods are based on the transformation without simplifications and assumptions of hydrodynamic equations into a form containing “non-primitive” variables and the demonstration of the possibilities of solving the equations. The GAMS programming language was used for approximate solutions for the first time. The aim of this paper is to demonstrate the possibility of solving the full equations in “non-primitive” variables for various conditions. The results showed the possibility of considering the compressibility of the medium when solving the inverse problem of hydrodynamics; the identity of solutions of the proposed system of equations and equations using the potential; and the possibility of using optimizing programming languages for hydrodynamics problems. The scientific novelty of this research consists of solving the full equations of hydrodynamics with the use of “non-primitive” variables but without the use of the current function. Doi: 10.28991/ESJ-2024-08-02-021 Full Text: PDF