Adaptive Time-Stepping for Incompressible Flow Part II: Navier-Stokes Equations
SIAM Journal on Scientific Computing
Fast iterative solvers for buoyancy driven flow problems
Journal of Computational Physics
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
Journal of Computational Physics
Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains
Computers & Mathematics with Applications
ALADINS: An ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations
Journal of Computational Physics
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Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams-Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution.