Journal Article10.1137/0723048
A semi-implicit method for hyperbolic problems with different time-scales
Jaime Guerra,Bertil Gustafsson +1 more
24
TL;DR: This paper analyzes the leap-frog backwards Euler scheme and shows, that when the ratio $\varepsilon $ between the slow and the fast scale tends to zero, the solutions of the approximation converge to Solutions of the reduced differential equation.
read more
Abstract: Hyperbolic systems with two different time-scales are considered, where the solutions vary on the slow scale only. For this type of problem semi-implicit difference methods are very natural, and in this paper we analyze the leap-frog backwards Euler scheme. In particular it is shown, that when the ratio $\varepsilon $ between the slow and the fast scale tends to zero, the solutions of the approximation converge to solutions of the reduced differential equation. Numerical experiments are included for illustration of the theoretical results.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Review of preconditioning methods for fluid dynamics
TL;DR: The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations and some applications for viscous flow are considered.
317
Semi-implicit and fully implicit shock-capturing methods for nonequilibrium flows
Helen C. Yee,Judy L. Shinn +1 more
TL;DR: Some numerical aspects of finite-differ ence algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed, and an implicit algorithm with explicit coupling between fluid and species equations is also proposed.
57
Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms
Helen C. Yee,Judy L. Shinn +1 more
- 01 Jan 1987
TL;DR: Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms with stiffNonhomogeneity terms are discussed, providing a more efficient solution procedure than one might have anticipated.
A numerical method for incompressible and compressible flow problems with smooth solutions
Jaime Guerra,Bertil Gustafsson +1 more
TL;DR: A semi-implicit difference method of second order in space is introduced for the numerical solution of the Euler equations if the Mach number e is small, and the solutions are second-order accurate also in time.
55
Iterative solution methods and preconditioners for block-tridiagonal systems of equations
Sverker Holmgren,Kurt Otto +1 more
TL;DR: Systems of equations arising from implicit time discretization and finite difference space discretizations of systems of partial differential equations in two space dimensions are considered.
43
References
Comparison of accurate methods for the integration of hyperbolic equations
Heinz-Otto Kreiss,Joseph Oliger +1 more
TL;DR: In this paper, the authors investigate more accurate difference methods and show that fourth order methods are optimal in some sense, and compare these methods with a variant of the Fourier technique.
674
Problems with Different Time Scales for Ordinary Differential Equations
TL;DR: In this paper, the authors consider a stiff nonlinear system and assume that the large eigenvalues of the system are purely imaginary, and conditions are given that the system has smooth solutions in long time intervals.
100
Initialization of the Primitive Equations by the Bounded Derivative Method
TL;DR: In this paper, the authors show that a solution of such a system which varies slowly with respect to time must have a number of time derivatives on the order of slow time scale.
Difference approximations of hyperbolic problems with different time scales. I : The reduced problem
TL;DR: Difference approximations of hyperbolic problems with different time scales are discussed in this paper, where the reduced problem is reduced to a reduced version of the original problem with a different time scale.
19
Asymptotic expansions for hyperbolic problems with different time-scales
TL;DR: Asymptotic expansions for the solution to hyperbolic systems with different time scales in one space dimension were derived in this paper for the general case with singular coefficients at the boundary.
16