Direct problem and inverse problem for the supersonic plane flow past a curved wedge

2011 ◽  
pp. n/a-n/a ◽  
Author(s):  
Libin Wang
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Plane Flow ◽  
Flow Past

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

scholarly journals On investigation of the inverse problem for a parabolic integro-differential equation with a variable coefficient of thermal conductivity

2020 ◽  
Vol 30 (4) ◽  
pp. 572-584
Author(s):  
D.K. Durdiev ◽  
J.Z. Nuriddinov
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Variable Coefficient ◽  
Direct Problem ◽  
Local Existence ◽  
Problem Solution ◽  
Volterra Type ◽  
Integral Term ◽  
Local Existence And Uniqueness ◽  
Coefficient Of Thermal Conductivity

The inverse problem of determining a multidimensional kernel of an integral term depending on a time variable $t$ and $ (n-1)$-dimensional spatial variable $x'=\left(x_1,\ldots, x_ {n-1}\right)$ in the $n$-dimensional heat equation with a variable coefficient of thermal conductivity is investigated. The direct problem is the Cauchy problem for this equation. The integral term has the time convolution form of kernel and direct problem solution. As additional information for solving the inverse problem, the solution of the direct problem on the hyperplane $x_n = 0$ is given. At the beginning, the properties of the solution to the direct problem are studied. For this, the problem is reduced to solving an integral equation of the second kind of Volterra-type and the method of successive approximations is applied to it. Further the stated inverse problem is reduced to two auxiliary problems, in the second one of them an unknown kernel is included in an additional condition outside integral. Then the auxiliary problems are replaced by an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the Hölder class of functions, we prove the main result of the article, which is a local existence and uniqueness theorem of the inverse problem solution.

scholarly journals Another point of view on proportional navigation

1998 ◽  
Vol 4 (3) ◽  
pp. 201-231
Author(s):  
E. Duflos ◽  
P. Penel ◽  
P. Vanbeeghe ◽  
P. Borne
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Point Of View ◽  
Proportional Navigation ◽  
Guidance Laws ◽  
The Way

Proportional navigation is one of the most popular and one of the most used of the guidance laws. But the way it is studied is always the same: the acceleration needed to reach a known target is derived or analyzed. This way of studying guidance laws is called “the direct problem” by the authors. On the contrary, the problem considered here is to find, from the knowledge of a part of the trajectory of a maneuvering object, the target of this object. The authors call this way of studying guidance laws “the inverse problem”.

Algorithm for Detecting Multiple Partial Blockages in Liquid Pipelines by Using Inverse Transient Analysis

SPE Journal ◽  
2021 ◽  
pp. 1-29
Author(s):  
C. Zhang ◽  
J. J. Zhang ◽  
C. B. Ma ◽  
G. E. Korobkov
Keyword(s):  
Inverse Problem ◽  
Crude Oil ◽  
Direct Problem ◽  
Pressure Response ◽  
Analytical Evaluation ◽  
Long Distance ◽  
Local Flow ◽  
Measuring Point ◽  
Detection Techniques ◽  
Oil Pipelines

Summary Partial blockages form on the inner wall of the crude-oil pipelines as a result of asphaltene precipitation, scale deposition, and so forth. If not controlled and rehabilitated periodically, these partial blockages can have a serious adverse effect on the efficiency, economy, and safety of the operation of the pipeline. Before each rehabilitation operation, the detection of the local flow-condition deterioration (change in diameter) is necessary for efficiency and economy considerations, especially for long-distance subsea crude-oil pipelines. Most conventional detection techniques require the installment of detecting devices along the pipeline. However, they are economically expensive and even technically impossible for pipelines in operation. The present work focuses on an economically efficient technique that can realize remote nonintrusive measurement (i.e., the pressure-wave technique). The purpose of our research is to develop a method for calibrating multiple irregular partial blockages inside the liquid pipe by using the pressure response in the time domain at certain measuring points along the pipe under the transient state. The method involves the direct problem and the inverse problem. The direct problem is the simulation of the transient flow in the liquid pipe with single or multiple partial blockages. A second-order direct problem solver is developed in the framework of the Godunov-typefinite-volume method (FVM). The inverse problem is to determine the partial-blockage distribution by using the pressure response at the measuring point under transient conditions. Our algorithm to solve the inverse problem comprises analytical evaluation and optimization. The analytical evaluation provides a reliable search space for the following optimization procedure, and thus effectively alleviates the local optimum problem. Numerical results demonstrate the efficiency and accuracy of proposed methods for solving the direct and inverse problems.

Analysis and Optimization of Diagnostic Procedures for Aviation Radioelectronic Equipment

2021 ◽  
pp. 948-972
Author(s):  
Maksym Zaliskyi ◽  
Oleksandr Solomentsev ◽  
Ivan Yashanov
Keyword(s):  
Inverse Problem ◽  
Probability Density Function ◽  
Health Monitoring ◽  
Direct Problem ◽  
Diagnostic Procedures ◽  
Operation System ◽  
Equipment Operation ◽  
Efficiency Estimation ◽  
Function Calculation ◽  
Simulation Results

In this chapter, the authors present the questions of aviation radioelectronic equipment operation. The structure of operation system is considered based on processes approach with adaptable control principles usage. Operation system contains processes of diagnostics and health monitoring. The authors consider the direct problem of efficiency estimation for diagnostics process, and main attention is paid to probability density function calculation for diagnostics duration. Simulation results were used for adequacy testing of these calculations. The authors also take into account the possibility of first and second kind errors presence. The inverse problem for diagnostics is defined and solved for mathematical expectation of repair time. In general case, the inverse problem can be solved for seven options of optimization.

scholarly journals Solution of inverse heat conduction equation with the use of Chebyshev polynomials

2016 ◽  
Vol 37 (4) ◽  
pp. 73-88 ◽  
Author(s):  
Magda Joachimiak ◽  
Andrzej Frąckowiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Direct Problem ◽  
Least Square Method ◽  
Least Square ◽  
Random Disturbance ◽  
Inverse Heat Conduction ◽  
Chebyshev Nodes ◽  
The Difference ◽  
The Stability

AbstractA direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.

scholarly journals Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Shiqin Lyu ◽  
Can Wu ◽  
Sufang Zhang
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
External Surface ◽  
Heat Conduction Problem ◽  
Main Idea ◽  
Inverse Heat Conduction Problem ◽  
Laminar Flows ◽  
Temperature Measurements ◽  
Control Technique ◽  
Unknown Boundary

The inverse heat conduction problem on the heat transfer characteristics of cooled/heated laminar flows through finite length thick-walled circular tubes is studied, using temperature measurements taken at several different locations within the fluid in this paper. The method of radial basis functions is coupled with the boundary control technique to estimate the unknown temperature on the external surface of the circular pipe. The main idea of the proposed method is to solve the direct problem instead of solving the inverse problem directly. The temperature data obtained from the direct problem are used to simulate the temperature measurement for the inverse problem, and during the calculation, the Tikhonov regularization and L-curve methods are employed to solve the inverse problem. Therefore, this study also considers the influence of errors in these measurements upon the precision of the estimated results as well as the influence of the locations and number of sensors used upon the accuracy of the estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.

Unsteady plane flow past curved obstacles with infinite wakes

1955 ◽  
Vol 229 (1177) ◽  
pp. 152-180 ◽  
Keyword(s):  
Unsteady Flow ◽  
Classical Theory ◽  
Steady Motion ◽  
Uniform Motion ◽  
Plane Flow ◽  
Flow Past ◽  
Long Duration ◽  
Infinite Extent ◽  
The Mean ◽  
Special Case

A theory of unsteady flow about obstacles behind which are wakes or cavities of infinite extent is developed for the case when the velocities and displacements of the unsteady perturbations about the mean steady motion are small. Unsteady Helmholtz flows (constant wake pressure) receive detailed attention both for general non-uniform motion and for the special case of harmonic motions of long duration. A number of possible applications of the theory to aerodynamic problems are indicated, the most important being the flutter of a stalled aerofoil. The classical theory of unsteady aerofoik motion is shown to be a special case of the theory given in this paper.

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