Regularization of the backward-in-time Kuramoto-Sivashinsky equation

DOI10.1016/j.cam.2009.12.032zbMath1273.65129arXiv1407.1731OpenAlexW2083804189MaRDI QIDQ964961

Jonathan Gustafsson, Bartosz Protas

Publication date: 21 April 2010

Published in: Journal of Computational and Applied Mathematics, Computers and Fluids (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1731

zbMATH Keywords

regularizationunbounded domainsfluid mechanicsspectral methodssteady Navier-Stokes systemwake flowsnumerical PDEsterminal value problems

Mathematics Subject Classification ID

Related Items (4)

A fourth-order numerical scheme for solving the modified Burgers equation ⋮ Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation ⋮ Well- and ill-posedness for a class of the \(3D\)-generalized Kuramoto-Sivashinsky equations ⋮ An improved iteration regularization method and application to reconstruction of dynamic loads on a plate

Uses Software

• LAPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains
• A reference solution of the flow over a circular cylinder at \(Re = 40\)
• Backward behavior of solutions of the Kuramoto-Sivashinsky equation
• The asymptotic form of the stationary separated circumfluence of a body at high Reynolds numbers
• Does the stationary viscous flow around a circular cylinder exist for large Reynolds numbers? A numerical solution via variational imbedding
• Second-order adaptive boundary conditions for exterior flow problems: Non-symmetric stationary flows in two dimensions
• Steady viscous flow past a circular cylinder up to Reynolds number 600
• The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
• The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
• On the errors incurred calculating derivatives using Chebyshev polynomials
• Family of spectral filters for discontinuous problems
• On the behavior of the solutions of the Kuramoto-Sivashinsky equation for negative time
• The final value problem for evolution equations
• Viscous flow past circular cylinders
• Numerical solution of problems in unbounded regions: coordinate transforms
• Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
• A comparison of some inverse methods for estimating the initial condition of the heat equation
• Roundoff error in computing derivatives using the Chebyshev differentiation matrix
• Entropy- and Tikhonov-based regularization techniques applied to the backwards heat equation
• Spectral methods for incompressible viscous flow
• Adaptive boundary conditions for exterior flow problems
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems
• On the linearized hydrodynamical equations in two dimensions
• On the stationary solutions of the Navier-Stokes equations in two dimensions
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Simple viscous flows: From boundary layers to the renormalization group
• Steady incompressible flow past a row of circular cylinders
• A proposal concerning laminar wakes behind bluff bodies at large Reynolds number
• A Nonstandard Approach to a Data Assimilation Problem and Tychonov Regularization Revisited
• Steady separated flow past a circular cylinder at low Reynolds numbers
• LAPACK Users' Guide
• Stability of the Fourier Method
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• A numerical study of steady viscous flow past a circular cylinder
• On the Comparison of Solutions of Related Properly and Improperly Posed Cauchy Problems for First Order Operator Equations
• The Fourier Method for Nonsmooth Initial Data
• Asymptotic Theory of Separated Flows
• ASYMPTOTIC BEHAVIOR FOR TWO REGULARIZATIONS OF THE CAUCHY PROBLEM FOR THE BACKWARD HEAT EQUATION
• High-Reynolds-number weakly stratified flow past an obstacle
• Solving Nonlinear Equations with Newton's Method
• Some steady vortex flows past a circular cylinder
• Numerical solution of the Navier–Stokes equations for the flow in a cylinder cascade
• Perspectives in Flow Control and Optimization
• Spectral Methods
• Spectral Methods
• Numerical Studies of Viscous Flow around Circular Cylinders
• Pseudoparabolic Partial Differential Equations
• Steady Two-Dimensional Viscous Flow of an Incompressible Fluid past a Circular Cylinder
• THE STEADY FLOW OF VISCOUS FLUID PAST A SPHERE AND CIRCULAR CYLINDER AT SMALL REYNOLDS NUMBERS
• On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon’s paradox
• RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
• Stability of viscous flow past a circular cylinder

This page was built for publication: Regularization of the backward-in-time Kuramoto-Sivashinsky equation