A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
On numerical differential algebraic problems with application to semiconductor device simulation
SIAM Journal on Numerical Analysis
An improvement of fractional step methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Projected implicit Runge-Kutta methods for differential-algebraic equations
SIAM Journal on Numerical Analysis
Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
Journal of Computational Physics
An analysis of the fractional step method
Journal of Computational Physics
Effects of the computational time step on numerical solutions of turbulent flow
Journal of Computational Physics
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
SIAM Journal on Numerical Analysis
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Structure Preservation for Constrained Dynamics with Super Partitioned Additive Runge--Kutta Methods
SIAM Journal on Scientific Computing
Computing flows on general three-dimensional nonsmooth staggered grids
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Journal of Computational Physics
Journal of Computational Physics
Analysis of an exact fractional step method
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
A robust high-order compact method for large eddy simulation
Journal of Computational Physics
Towards the ultimate variance-conserving convection scheme
Journal of Computational Physics
A numerical method for large-eddy simulation in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Journal of Computational Physics
A staggered grid, high-order accurate method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Time-reversibility of the Euler equations as a benchmark for energy conserving schemes
Journal of Computational Physics
Energy-preserving integrators for fluid animation
ACM SIGGRAPH 2009 papers
Contractivity/monotonicity for additive Runge--Kutta methods: Inner product norms
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
Hi-index | 31.46 |
Energy-conserving methods have recently gained popularity for the spatial discretization of the incompressible Navier-Stokes equations. In this paper implicit Runge-Kutta methods are investigated which keep this property when integrating in time. Firstly, a number of energy-conserving Runge-Kutta methods based on Gauss, Radau and Lobatto quadrature are constructed. These methods are suitable for convection-dominated problems (such as turbulent flows), because they do not introduce artificial diffusion and are stable for any time step. Secondly, to obtain robust time-integration methods that work also for stiff problems, the energy-conserving methods are extended to a new class of additive Runge-Kutta methods, which combine energy conservation with L-stability. In this class, the Radau IIA/B method has the best properties. Results for a number of test cases on two-stage methods indicate that for pure convection problems the additive Radau IIA/B method is competitive with the Gauss methods. However, for stiff problems, such as convection-dominated flows with thin boundary layers, both the higher order Gauss and Radau IIA/B method suffer from order reduction. Overall, the Gauss methods are the preferred method for energy-conserving time integration of the incompressible Navier-Stokes equations.