Formation of one-dimensional flows of a heat-conducting viscous gas

1976 ◽  
Vol 10 (4) ◽  
pp. 659-663 ◽  
Author(s):  
A. I. Igoshin
Keyword(s):  
Heat Conducting ◽  
Viscous Gas ◽  
One Dimensional

Joint State and Input Estimation for One-Dimensional Heat Conduction

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Sangeeta Nundy ◽  
Siddhartha Mukhopadhyay ◽  
Alok Kanti Deb
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Estimation Algorithm ◽  
Inverse Heat Conduction Problem ◽  
Least Square ◽  
Heat Conducting ◽  
Orthogonal Collocation ◽  
Input Estimation ◽  
One Dimensional ◽  
Joint State

This paper presents a joint state and input estimation algorithm for the one-dimensional heat-conduction problem. A computationally efficient method is proposed in this work to solve the inverse heat-conduction problem (IHCP) using orthogonal collocation method (OCM). A Kalman filter (KF) algorithm is used in conjunction with a recursive-weighted least-square (RWLS)-based method to simultaneously estimate the input boundary condition and the temperature field over the heat-conducting element. A comparison study of the algorithm is shown with explicit finite-difference method (FDM) of approximation and analytical solution of the forward problem, which clearly reveals the high accuracy with lower-dimensional modeling. The estimation results show that the performance of the estimator is robust to noise sensitivity up to a certain level, which is practically acceptable.

scholarly journals Fourth-Order Deferred Correction Scheme for Solving Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Yambangwai ◽  
N. P. Moshkin
Keyword(s):  
Fourth Order ◽  
Heat Conduction Problem ◽  
Correction Method ◽  
Dirichlet Boundary Conditions ◽  
Heat Conducting ◽  
One Dimensional ◽  
Deferred Correction ◽  
The Stability ◽  
The One ◽  
Nicolson Scheme

A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nicolson scheme for the numerical solution of the one-dimensional heat equation. The fourth-order methods proposed are the easier development and can be solved by using Thomas algorithms. The stability analysis and numerical experiments have been limited to one-dimensional heat-conducting problems with Dirichlet boundary conditions and initial data.

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