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Statistical Second-order Two-scale Method for Nonstationary Coupled Conduction-Radiation Heat Transfer Problem of Random Porous Materials
Get PDFThis paper develops a novel statistical second-order two-scale (SSOTS) method to predict the heat transfer performances of three-dimensional (3D) porous materials with random distribution. Firstly, the mesoscopic configuration for the structure with random distribution is briefly characterized Secondly, the SSOTS formulas for calculating effective thermal conductivity parameters, temperature field and heat flux densities are derived by means of construction way. Then, the algorithm procedure based on the SSOTS method is described in details. Finally, numerical results for porous materials with varying probability distribution models are calculated by SSOTS algorithm, and compared with the data by finite element method (FEM) in a very fine mesh and theoretical methods. They show that the SSOTS method is not only valid, but also accurate to predict the coupled heat transfer performances of random porous materials and demonstrate its potential applications in thermal engineering
Thermal Radiation and Chemical Reaction Effects on Steady Convective Slip Flow with Uniform Heat and Mass Flux in the Presence of Ohmic Heating and a Heat Source
No full textThis study deals with the investigation of the effects exerted by heat radiation and a first-order chemical reaction on the magnetohydrodynamics boundary layer slip flow which is established past a vertical permeable surface embedded in a porous medium (with uniform heat and mass flux). The heat equation includes the relevant terms, i.e. the viscous dissipation, radiative heat flux, Ohmic dissipation, and absorption of radiation. The mass transfer equation takes into account the effects related to the chemically reactive species. A classical model for optically thin media is used for studying the effect of radiation. The resulting non-linear coupled partial differential equations are solved by a perturbation technique. The results show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reactions, thermal stratification and the imposed magnetic field. The effects of various parameters on the skin-friction coefficient are also assessed
Space-time Discontinuous Galerkin Method Based on a New Generalized Flux Vector Splitting Method for Multi-dimensional Nonlinear Hyperbolic Systems
Get PDFThe space-time discontinuous Galerkin method for multi-dimensional nonlinear hyperbolic systems is enhanced with a generalized technique for splitting a flux vector that is not limited to the homogeneity property of the flux. This technique, based on the flux’s characteristic decomposition, extends the scope of the method’s applicability to a wider range of problems, including elastodynamics. The method is used for numerical solution of a number of representative problems based on models of vibrating string and vibrating rod that involve the propagation of a sharp front through the solution domain
A High-Order Finite-Difference Scheme with a Linearization Technique for Solving of Three-Dimensional Burgers Equation
Get PDFThe objective of this paper aims to present a numerical solution of high accuracy and low computational cost for the three-dimensional Burgers equations. It is a well-known problem and studied the form for one and two-dimensional, but still little explored numerically for three-dimensional problems. Here, by using the High-Order Finite Difference Method for spatial discretization, the Crank-Nicolson method for time discretization and an efficient linearization technique with low computational cost, two numerical applications are used to validate the proposed formulation. In order to analyze the numerical error of the proposed formulation, an unpublished exact solution was used
Novel Iterative Algorithms Based on Regularization Total Least Squares for Solving the Numerical Solution of Discrete Fredholm Integral Equation
Get PDFDiscretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov regularization TLS problem to an unconstrained optimization problem with the properties of a convex function. The optimization problem will be solved with the state-of-the-art conjugate gradient (CG) method, and moreover, the adaptive strategy for selecting regularization parameter is also established. Finally, both the new methods are applied to tackle several Fredholm integral equations of the first kind which are known to be typical ill-posed problems. The results of numerical examples demonstrate that the robustness and effectiveness of the two novel algorithms make a significant improvement in the solution of ill-posed linear problems, i.e., yield more accurate regularized solution than other typical methods
Speedup of Elastic–Plastic Analysis of Large-scale Model with Crack Using Partitioned Coupling Method with Subcycling Technique
Get PDFTo speed up the elastic–plastic analysis of a large-scale model with a crack in which plasticity is observed near the crack, the partitioned coupling method is applied. In this method, the entire analysis model is decomposed into two non-overlapped domains (i.e., global and local domains), and the two domains are analyzed with an iterative method. The cracked local domain is modeled as an elastic–plastic body, whereas the large-scale global domain is modeled as an elastic body. A subcycling technique is utilized for incremental analysis to reduce the number of global elastic analyses. For a benchmark problem with 6 million degrees of freedom, the developed partitioned coupling solver with the subcycling technique was 3.34 times faster than the developed conventional FEM solver
An Artificial Boundary Method for Burgers’ Equation in the Unbounded Domain
Get PDFIn this paper, we construct a numerical method for one-dimensional Burgers’ equation in the unbounded domain by using artificial boundary conditions. The original problem is converted by Hopf-Cole transformation to the heat equation in the unbounded domain, the latter is reduced to an equivalent problem in a bounded computational domain by using two artificial integral boundary conditions, a finite difference method with discrete artificial boundary conditions is established by using the method of reduction of order for the last problem, and thereupon the numerical solution of Burgers’ equation is obtained. This artificial boundary method is proved and verified to be uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time for solving Burgers’ equation on the computational domain
Structural Topology Optimization Based on the Level Set Method Using COMSOL
Get PDFIn order to obtain smooth boundary and improve computational efficiency, a new topology optimization scheme based on the level set method is presented. Using the level set function as design variable and the volume ratio of the solid material as volume constraint, respectively, this scheme can easily implement compliance minimization structure topology optimization in associated with the reaction-diffusion equation in commercial software COMSOL. Compared with the results of solid isotropic material with penalization (SIMP) and traditional level set method, this scheme obtained a smooth geometry boundary. In the present computational scheme, the computational cost could be enormously saved without solving the complicated Hamilton-Jacobi equation restricted by Courant-Friedrichs-Lewy (CFL) condition. Two numerical examples verified the performance of the proposed structural topology optimization scheme
A Wavelet Method for Solving Bagley-Torvik Equation
Get PDFIn this paper, an efficient and robust wavelet Laplace inversion method of solving the fractional differential equations is proposed. Such an inverse function can be applied to any reasonable function categories and it is not necessary to know the properties of original function in advance. As an example, we have applied the proposed method to the solution of the Bagley–Torvik equations and Numerical examples are given to demonstrate the efficiency and accuracy of the proposed
On the Formulation of Three-Dimensional Inverse Catenary for Embedded Mooring Line Modeling
Get PDFEmbedded anchors have been widely used in offshore operations, and they are known to be effective and economical solutions to anchoring problems. Aiming at contributing to the definition and understanding of the embedded mooring line behavior, this paper expands the formulation adopted at DNV Recommended Practices, for two-dimensional modeling of the interaction between the seabed and the anchor line, to three-dimensional analysis. The formulation here presented, within an elegant differential geometry approach, can now model even out of plane lines. A reference problem is then defined and solved using the obtained governing equations. Corresponding equations are implemented and solved numerically in MATLAB® environment. Numerical results are also presented and discussed