Sergei Utyuzhnikov

Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization

Optimization is one of the most important and challenging parts of any engineering design. In real-world design, multiobjective optimization with constraints has to be considered. The optimal solution in this case is not unique because the objectives can contradict each other. Therefore, a set of optimal solutions, which forms the Pareto frontier, should be considered. There are many algorithms to generate a Pareto set. However, only a few of them are potentially capable of providing an evenly distributed set of solutions. This property is especially important in real-life design because a decision maker is usually able to analyse only a very limited number of solutions. The main objective of this article is to develop and give detailed description of an algorithm that is able to generate an evenly distributed Pareto set in a general formulation. The approach is based on shrinking a search domain to generate a Pareto optimal solution in a selected area on the Pareto frontier. The effectiveness of the algorithm is demonstrated by a number of challenging test cases. For the first time, some of these test cases are successfully solved via a classical approach.

Inverse source problem and active shielding for composite domains

The problem of active shielding (AS) for a multiply connected domain consists of constructing additional sources of the field (e.g., acoustic) so that all individual subdomains can either communicate freely with one another or otherwise be shielded from their peers. This problem can be interpreted as a special inverse source problem for the differential equation (or system) that governs the field. In the paper, we obtain general solution for a discretized composite AS problem and show that it reduces to solving a collection of auxiliary problems for simply connected domains. c

Stabilization of a Hypersonic Boundary Layer Using a Wavy Surface

Stability of a supersonic near-wall flow over a shallow grooved plate in the freestream of Mach 6 is investigated by means of numerical simulations and wind-tunnel experiments. Numerical solutions of two-dimensional Navier–Stokes equations are used to model propagation of artificial disturbances of several fixed frequencies generated by an actuator placed on the wall. It is shown that the high-frequency forcing excites unstable waves in the flat-plate boundary layer. These waves are relevant to the second-mode instability. The wavy wall damps the disturbances in a high-frequency band while it enhances them at lower frequencies. Stability experiments are conducted in the Institute of Theoretical and Applied Mechanics Tranzit-M shock tunnel under natural freestream conditions. The measured disturbance spectra are similar to those predicted numerically. They contain a peak associated with the second-mode instability. This peak is damped by the wavy wall, while a marginal increase of the disturbance amplitude...

Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions

The paper is devoted to the further development and systematic performance evaluation of a recent deterministic framework Nesvetay-3D for modelling three-dimensional rarefied gas flows. Firstly, a review of the existing discretization and parallelization strategies for solving numerically the Boltzmann kinetic equation with various model collision integrals is carried out. Secondly, a new parallelization strategy for the implicit time evolution method is implemented which improves scaling on large CPU clusters. Accuracy and scalability of the methods are demonstrated on a pressure-driven rarefied gas flow through a finite-length circular pipe as well as an external supersonic flow over a three-dimensional re-entry geometry of complicated aerodynamic shape.

Experimental Validation of the Active Noise Control Methodology Based on Difference Potentials

To achieve active noise cancellation over a large area, it is often necessary to get a measure of the physical properties of the noise source to devise a counter measure. This, however, is not practical in many cases. A mathematical approach, the Difference Potential Method, can provide an alternative solution for active shielding over a large area. In this approach, the cancellation of unwanted noise requires only measurements near the boundary surface but not at the source itself, and it does not require any other information. Moreover, the solution based on difference potentials applies to bounded domains in the presence of acoustic sources inside the domain to be shielded. This paper reports on the results of experimental validation. It has been demonstrated that while preserving the wanted sound, the developed approach can cancel out the unwanted noise. The volumetric noise cancellation offered by the proposed methodology along with leaving the wanted sound unchanged is a unique feature compared to other techniques available in the literature. It can be most useful in the context of applications related to civil aviation, in particular, for eliminating the exterior noise inside the passenger compartments of both current and future generation of commercial aircraft.

Numerical modeling of combustion of fuel-droplet-vapour releases in the atmosphere

The paper is concerned with a numerical simulation of fuel cloud behaviour which follows releases of a liquid fuel. The main aim of the work is to develop further a mathematical model to simulate such releases into the atmosphere. The model is validated by a comparison with experimental results. The influence of boundary conditions for turbulent kinetic energy k and its dissipation rate ε on the solution is investigated. It is concluded that the solution depends mainly on the combination of k and ε in the form k3/2/ε rather than each of these values separately. A way to define the boundary conditions for k and ε is suggested. The KIVA-II code has been used as the base of the code used. The original code has been modified to simulate low Mach number atmospheric flows, radiation, soot formation and turbulent combustion.

Non-stationary problem of active sound control in bounded domains

The nonstationary problem of active shielding of some domain from the effect of the sources distributed in another domain is considered.The active shielding is realized via the implementation of additional sources in such a way that the total contribution

Efficient numerical method for simulation of supersonic viscous flow past a blunted body at a small angle of attack

Abstract For solving the three-dimensional (3-D) full viscous shock-layer (FVSL) equations in a body-oriented coordinate system, an asymptotic method is used with the angle of attack as a small parameter. In using a small parameter method, the (3-D) FVSL system is separated into an axisymmetric set and a linear 2-D set of equations. The method of global iterations was used to solve both the axisymmetric and linearized sets of equations. Global iterations were carried out on the pressure gradient tangential component and on the shock wave tangle. The method is used uniformly for both the blunted and conic parts of the body. The shock wave angle was found by using the Rankine-Hugoniot boundary condition for the normal component of the velocity. A computational grid adapted to the solution was used in solving both systems of equations. The comparison of this approach with 3-D implicit time-marching methods shows that the time neccessary for the calculation in the 3-D case is about 100 times less, while the accuracy of the calculations is essentially the same. Also, the small parameter method enables one to find a one-parameter family of solutions; the parameter in question is the angle of attack.

A numerical method for solving the equations of a viscous shock layer

Abstract A method is proposed for calculating supersonic flows around blunt bodies. This is based on the numerical solution of the complete two-dimensional equations of a viscous shock layer. Allowance for the upward transfer of disturbances through the stream into the subsonic regions is ensured by carrying out global iterations along the whole of the segment of the shock layer considered. Each global iteration is calculated by the marching method. Questions regarding the stability of iterative process are considered as well as the correctness of the formulation of the mixed problem on each global iteration. The results of the calculations are in good agreement with experimental data.

Variational method for untangling and optimization of spatial meshes

A variational method that can provably construct 3D quasi-isometric mappings between domains of a complex shape is introduced. A local maximum principle for polyconvex mesh element distortion measures is formulated. It allows us to control the invertibility and distortion bounds for non-simplicial elements in the minimization process. A simple and efficient technique for construction of boundary orthogonal meshes suggested in Garanzha (2000) is applied to the construction of hexahedral meshes and thick prismatic mesh layers around complex shapes. The mesh untangling technique, which is a generalization of the penalty method suggested in Garanzha and Kaporin (1999), is verified on a wide set of challenging test problems. Another untangling technique based on theoretical ideas from Ivanenko (1997) is implemented and tested. It provably constructs admissible meshes using a finite number of minimization steps. A minimization technique for the mesh distortion functional is described. The approach is based on the global gradient search technique with preconditioning and domain decomposition for local mesh optimization and untangling. Application areas for explicit and implicit minimization methods are evaluated.