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From now on, we let L m (Q, h, H) be a real symmetric problem.
In the product formula algorithm, the mechanical and thermal problems are solved separately, resulting in a symmetric problem.
The formulation has also been included in a 3D cylindrically symmetric problem of two colliding spherical shocks.
We first test the method on a radially symmetric problem where the exact vorticity is known for all time.
Our methodology entails linearizing the compressible Euler equations for mass and momentum conservation about a cylindrically symmetric problem and analysing the perturbed profiles at different mode numbers.
This is an axially symmetric problem, identical to our earlier work [35], and we get the same results, shown in Figs. 5 and 6.
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Such problems include the class of block- symmetric problems of discrete programming.
Let L m (h, H, Q) and L ( h ̃, H ̃, Q ̃ ) be two real symmetric problems.
Assuming that L m (Q, h, H) and L m ( Q ̃, h ̃, H ̃ ) are two real symmetric problems.
New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH.
Several examples are considered to demonstrate the convergence properties of the three schemes, but attention is limited to spherically symmetric problems such as the one-dimensional point explosion.
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