This paper is to study extension of high resolution kinetic flux-vector splitting (KFVS) methods. In this new method, two Maxwellians are first introduced to recover the Euler equations with an additional conservative...
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This paper is to study extension of high resolution kinetic flux-vector splitting (KFVS) methods. In this new method, two Maxwellians are first introduced to recover the Euler equations with an additional conservative equation. Next, based on the well-known connection between the Euler equations and Boltzmann equations, a class of high resolution KFVS methods are presented to solve numerically multicomponent flows. Our method does not solve any Riemann problems, and add any nonconservative corrections. The numerical results are also presented to show the accuracy and robustness of our methods. These include one-dimensional shock tube problem, and two-dimensional interface motion in compressible flows. The computed solutions are oscillation-free near material fronts, and produce correct shock speeds.
In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using...
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In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and *** is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh ***. the latter can not be used in this case.
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