Showing papers by "Eli Turkel published in 2018"
TL;DR: This work considers fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound, and demonstrates that usually this is much more efficient than lower order schemes despite being implicit and only conditionally stable.
Abstract: We consider fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound. We demonstrate that usually this is much more efficient than lower order schemes despite being implicit and only conditionally stable. Fast time marching of the implicit scheme is accomplished by iterative methods such as conjugate gradient and multigrid. For conjugate gradient, an upper bound on the convergence rate of the iterations is obtained by eigenvalue analysis of the scheme. The implicit discretization technique is such that the spatial and temporal convergence orders can be adjusted independently of each other. In special cases, the spatial error dominates the problem, and then an unconditionally stable second order accurate scheme in time with fourth order accuracy in space is more efficient. Computations confirm the design convergence rate for the inhomogeneous, variable wave speed equation and also confirm the pollution effect for these time dependent problems.
42 citations
TL;DR: This work solves the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time using an implicit finite difference scheme and solving an elliptic equation at each time step by the method of difference potentials (MDP).
30 citations
TL;DR: The Huygens' principle is used to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time, and the resulting boundary equation is solved efficiently by the method of difference potentials (MDP).
14 citations
TL;DR: This work investigates the Runge–Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows, and focuses on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian.
13 citations
7 citations
TL;DR: It is concluded that augmentation improves the identification performance, in particular in the presence of noisy measurements, in some cases augmented TR succeeds in the identification whereas non-augmented TR fails.
6 citations
20 Jun 2018
TL;DR: In this article, the convective wave equation deals with wave propagation in a moving media, where convective element is the flow of water inside a river, along with a convective flow.
Abstract: The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along...
3 citations