These values were of the order of twice the overpressure and flame speed with a double obstacle separated 2.75 m (83 characteristic obstacle length scales) apart.
We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering.
We give local boundedness for very weak solutions of double obstacle problems.
This article mainly concerns double obstacle problems for second order divergence type elliptic equation divA x, u, ▽u) = divf(x).
end{aligned} (8 Owing to its governing influence on the finite interface width and its subsequent computational advantage, the double obstacle potential is used in all simulations of the present work.
In contrast to the double well potential, which is mostly used in the phase-field community, the double obstacle potential begin{aligned} w^{ob} phi )= {left{ begin{array}{ll} frac{16}{pi ^2}phi (1-phi ), &quad phi in mathcal {G} infty, &quadtext {else} end{array}right.
Beneficial for the double obstacle potential is the corresponding one-dimensional equilibrium phase-field profile, which is expressed as follows: begin{aligned} phi ^{ob}_{eq}(x) = {left{ begin{array}{ll} 0, &quad x < -0.125pi ^2epsilon, 0.5left(1+sin left({frac{4x}{pi epsilon }}right)right ), &quad x in [-0.125,0.125]pi ^2epsilon, 1, &quad x >0.125pi ^2epsilon end{array}right.
It is demonstrated in two-dimensional simulations of dendritic growth that a specific set of polynomials must be employed to achieve high accuracy in the models with double-well and double-obstacle potentials.
An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn Hilliard/Navier Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed.
My life is not a Double Dare obstacle course and I am not the happy child beaming for the cameras under a cascade of slime.
