Ghoamreza Shahriar Heshmati; Bahman Mehri
Abstract
In this paper a method is presented in details to solve a nonlinear partial differential equation which has many applications in engineering fields. The boundary condition is mixed to be able to define the value of function on its variation on the boundary. Examples are given to demonstrate the accuracy ...
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In this paper a method is presented in details to solve a nonlinear partial differential equation which has many applications in engineering fields. The boundary condition is mixed to be able to define the value of function on its variation on the boundary. Examples are given to demonstrate the accuracy and efficiency of the method.
Fereydoun Sabet Ghadam; Vahid Esfahanian; Mohammad Eftekhari Yazdi
Abstract
Capability of the Proper Orthogonal Decomposition (POD) method in extraction of the coherent structures from a spatio-temporal chaotic field is assessed in this paper. As the chaotic field, an ensemble of 40 snapshots, obtained from Direct Numerical Simulation (DNS) of the Kuramoto-Sivashinsky (KS) equation, ...
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Capability of the Proper Orthogonal Decomposition (POD) method in extraction of the coherent structures from a spatio-temporal chaotic field is assessed in this paper. As the chaotic field, an ensemble of 40 snapshots, obtained from Direct Numerical Simulation (DNS) of the Kuramoto-Sivashinsky (KS) equation, has been used. Contrary to the usual methods, where the ergodicity of the field is needed, the ensemble members are generated directly by disturbing the initial conditions in a random fashion. The POD eigenvalues and eigenmodes are extracted, using the POD/SVD technique and an ensemble averaging process is performed on the resulting modes, which are used in reconstruction of the field. The resulted mean field is compared with the Fourier mean field as well as the original (instantaneous) field. The results strictly have shown presence of non-coherent parts in the POD reconstructed field, which can be interpreted as the POD weakness in the filtering of the random part of the field. On the other hand, the ensemble averaged POD modes had obvious superiority, in comparison with the mean Fourier modes, in tracing of the mean behavior of the field and the mean temporal gradients. As a consequence, use of the ensemble averaging in the POD modes can be suggested, at least in some spatio-temporal the fields with dominant coherent structures.
