Semi-implicit projection methods for incompressible flow based on spectral deferred corrections

Authors:
Michael L. Minion
Affiliations:
Department of Mathematics, University of North Carolina, Phillips Hall, CB 3250, Chapel Hill, NC
Venue:
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Year:
2004

Citing 24
Cited 9

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations

Numerische Mathematik
Spectral integration and two-point boundary value problems

SIAM Journal on Numerical Analysis
Multilevel projection methods for partial differential equations

Multilevel projection methods for partial differential equations
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Implicit-explicit methods for time-dependent partial differential equations

SIAM Journal on Numerical Analysis
The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: a study of the boundary error

SIAM Journal on Scientific Computing
An impulse-based approximation of fluid motion due to boundary forces

Journal of Computational Physics
On the Removal of Boundary Errors Caused by Runge--Kutta Integration of Nonlinear Partial Differential Equations

SIAM Journal on Scientific Computing
Finite difference schemes for incompressible flows in the velocity-impulse density formulation

Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

Applied Numerical Mathematics - Special issue on time integration
The Correct Formulation of Intermediate Boundary Conditions for Runge--Kutta Time Integration of Initial Boundary Value Problems

SIAM Journal on Scientific Computing
Hamilton-based Numerical Methods for a Fluid-Membrane Interaction in Two and Three Dimensions

SIAM Journal on Scientific Computing
The blob projection method for immersed boundary problems

Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations

Journal of Computational Physics
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations

Recent trends in numerical analysis
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A New Fast-Multipole Accelerated Poisson Solver in Two Dimensions

SIAM Journal on Scientific Computing
Deferred Correction Methods for Initial Boundary Value Problems

Journal of Scientific Computing
Deferred Correction in Space and Time

Journal of Scientific Computing
Stability of W-methods with applications to operator splitting and to geometric theory

Applied Numerical Mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations

Applied Numerical Mathematics
Avoiding order reduction of fractional step Runge-Kutta discretizations for linear time dependent coefficient parabolic problems

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
High-order multi-implicit spectral deferred correction methods for problems of reactive flow

Journal of Computational Physics

Accelerating the convergence of spectral deferred correction methods

Journal of Computational Physics
A second-order boundary-fitted projection method for free-surface flow computations

Journal of Computational Physics
Error estimates for deferred correction methods in time

Applied Numerical Mathematics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties

Journal of Computational Physics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics

Journal of Computational Physics
On the choice of correctors for semi-implicit Picard deferred correction methods

Applied Numerical Mathematics
Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

SIAM Journal on Scientific Computing
A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation

SIAM Journal on Scientific Computing
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme

Journal of Computational Physics

Quantified Score

Hi-index	0.02

Visualization

Abstract

A semi-implicit form of spectral deferred corrections is used in a method of lines approach to create a projection method that is sixth-order accurate in both time and space for simple domains. The derivation of spectral deferred corrections is presented and compared to traditional deferred correction methods. An auxiliary variable form of the equations for Boussinesq flow is presented which facilitates a method of lines approach. A discussion of how these methods can be extended to complex spatial domains through the use of integral equation methods is also presented.