• International Journal of Aeronautical and Space Sciences
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• v.14 no.4
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• pp.387-397
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• 2013

An assessment of two-equation turbulence models, the low Reynolds k-${\varepsilon}$ and k-${\omega}$ SST models, with the compressibility corrections proposed by Sarkar and Wilcox, has been performed. The compressibility models are evaluated by investigating transonic or supersonic flows, including the arc-bump, transonic diffuser, supersonic jet impingement, and unsteady supersonic diffuser. A unified implicit finite volume scheme, consisting of mass, momentum, and energy conservation equations, is used, and the results are compared with experimental data. The model accuracy is found to depend strongly on the flow separation behavior. An MPI (Message Passing Interface) parallel computing scheme is implemented.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.