Rigid-Body Analysis of a Beveled Shape Structure in Regular Waves Using the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) Method

In many cases of wave structure interactions, three-dimensional models are used to demonstrate real-life complex environments in large domain scales. In the seakeeping context, predicting the motion responses in the interaction of a long body resembling a ship structure with regular waves is crucial and can be challenging. In this work, regular waves interacting with a rigid floating structure were simulated using the open-source code based on the weakly compressible smoothed particle hydrodynamics (WCSPH) method, and optimal parameters were suggested for different wave environments. Vertical displacements were computed, and their response amplitude operators (RAOs) were found to be in good agreement with experimental, numerical, and analytical results. Discrepancies of numerical and experimental RAOs tended to increase at low wave frequencies, particularly at amidships and near the bow. In addition, the instantaneous wave contours of the surrounding model were examined to reveal the effects of localized waves along the structure and wave dissipation. The results indicated that the motion response from the WCSPH responds well at the highest frequency range (ω > 5.235 rad/s).

Application of the Riemann problem with complex equations of state for modeling three-dimensional flows of real media

The paper considers the numerical simulation of spatial flows of real media in safety valves on the basis of the problem of an arbitrary discontinuity breakdown with complex equations of state. The solution is constructed by means of the developed numerical method, which is a modification of the classical scheme by S. K. Godunov and includes various complex equations of state of matter. The Van der Waals equations of state were used to model the flow of real gases, and the Mie-Grüneisen equation was used to describe the flow of a real weakly compressible fluid. It is shown that the proposed numerical schemes allow for modeling fluid and gas dynamic processes in real fluids and gases with shock waves and contact discontinuities and can be used both in areas of classical medium behavior and in areas with non-classical behavior.

Mechanical-Geometrical Modeling Of The Hyperelastic Materials At Uniaxial Stretching

Hyperelastic materials, such as rubber, occupy an important place in the design and operation of various technological equipment and machines. The article analyzed the deformation behavior of hyperelastic materials using a mechanical-geometric model. The method of mechanical-geometric modeling is a new method for obtaining constitutive relations and strain energy density functions for nonlinear elastic solids. It is based on physically and geometrically consistent prerequisites. The resulting models can describe broad classes of nonlinear elastic materials (both isotropic and anisotropic) depending on the mechanical and geometric properties “embedded” in them at the first stages of design. This paper discusses two basic types of models based on different initial geometry. The mechanical parameters of the models are constants, and the models themselves are considered in a statement corresponding to isotropic hyperelastic materials. The article presents the most common diagrams of deformation of artificial and natural rubbers, as well as steel. Hyperelastic materials, depending on the task, can be described in the nonlinear theory of elasticity as ideal incompressible, or as weakly compressible. Parameters of expressions of strain energy density functions of mechanical-geometric models obtained for cases of incompressible and weakly compressible continuous solids were identified. Stretch diagrams and diagrams of the transverse deformation function of the obtained mechanical-geometric models for the two cases mentioned above are plotted. The extension diagram for the model with parameters corresponding to the classic structural material of the steel type is also shown. Comments are given on the possibility of further paths of developing the method of mechanical-geometric modeling to obtain results not only in the field of nonlinear theory of elasticity, but also viscoelasticity.

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

Comparison between the Lagrangian and Eulerian Approach for Simulating Regular and Solitary Waves Propagation, Breaking and Run-Up

The present paper places emphasis on the most widely used Computational Fluid Dynamics (CFD) approaches, namely the Eulerian and Lagrangian methods each of which is characterized by specific advantages and disadvantages. In particular, a weakly compressible smoothed particle (WCSPH) model, coupled with a sub-particle scale (SPS) approach for turbulent stresses and a new depth-integrated non-hydrostatic finite element model were employed for the simulation of regular breaking waves on a plane slope and solitary waves transformation, breaking and run-up. The validation of the numerical schemes was performed through the comparison between numerical and experimental data. The aim of this study is to compare the two modeling methods with an emphasis on their performance in the simulation of hydraulic engineering problems.