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Additional info for Computational Science and Its Applications – ICCSA 2016: 16th International Conference, Beijing, China, July 4-7, 2016, Proceedings, Part I

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3◦ emanating from the leading edge of the wedge, as shown in Fig. 2. The computational domain is a square with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. 30475 9 (11) Fig. 2. Oblique shock problem description Here M is the Mach number and p is the pressure. Four Dirichlet boundary conditions are imposed at the left and the top boundaries, the condition v = 0 is set at the bottom boundary, and no boundary condition is imposed at the outflow (right) boundary. For all simulations we consider an unstructured mesh consisting of 462 nodes and 846 elements.

1 Analysis of Model (1) Fixed Points and Their Stability The system yn xn+1 = Axn 1+y n xn yn+1 = Byn 1+x n 1 1 has two fixed points (0, 0) and ( B−1 , A−1 ) that is positive when A > 1 and B > 1. Dynamical Behavior of a Cooperation Model with Allee Effect 39 1 1 The positive fixed point ( B−1 , A−1 ) is always saddle (Fig. 3). The other fixed point (0, 0) is always locally asymptotically stable because 00 00 J(0, 0) = Since both eigenvalues are zero (Fig. 1, Fig. 2 and Fig. 3). 2 Stability via Lyapunov Function In order to check the global stability, we use a Lyapunov function of the map F x y = y Ax 1+y x By 1+x Let V (x, y) = xy is the corresponding positive definite Lyapunov function (Fig.

The subgrid velocity field was determined by requiring the minimum of the associated kinetic energy for which the residue of the resolved scale solution vanishes on each element of the discretization. The idea of adding a nonlinear diffusion in both scales (subgrid and coarse) of the discretization was considered in [2] through the Dynamic Diffusion (DD) method, where the subgrid space is constructed by bubbles functions defined into elements and the amount of nonlinear diffusion is similar to the method presented in [15].

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