Boundary conditions for incompressible flows
Journal of Scientific Computing
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
Applied numerical linear algebra
Applied numerical linear algebra
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Symplectic Methods Based on Decompositions
SIAM Journal on Numerical Analysis
A new type of singly-implicit Runge-Kutta method
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
A staggered grid, high-order accurate method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Optimization of geometric multigrid for emerging multi- and manycore processors
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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In this follow-up of our previous work [30], the author proposes a high-order semi-implicit method for numerically solving the incompressible Navier-Stokes equations on locally-refined periodic domains. Fourth-order finite-volume stencils are employed for spatially discretizing various operators in the context of structured adaptive mesh refinement (AMR). Time integration adopts a fourth-order, semi-implicit, additive Runge-Kutta method to treat the non-stiff convection term explicitly and the stiff diffusion term implicitly. The divergence-free condition is fulfilled by an approximate projection operator. Altogether, these components yield a simple algorithm for simulating incompressible viscous flows on periodic domains with fourth-order accuracies both in time and in space. Results of numerical tests show that the proposed method is superior to previous second-order methods in terms of accuracy and efficiency. A major contribution of this work is the analysis of a fourth-order approximate projection operator.