Klaij 2021a - Revision history

Scipediacontent at 18:46, 11 March 2021

2021-03-11T18:46:01Z

Scipediacontent: Scipediacontent moved page Draft Content 631961461 to Klaij 2021a

2021-03-11T16:16:03Z

Scipediacontent moved page Draft Content 631961461 to Klaij 2021a

Scipediacontent: Created page with "== Abstract == Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local trunc..."

2021-03-11T16:16:01Z

Created page with "== Abstract == Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local trunc..."

New page

== Abstract ==

Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local truncation error. Significant savings in computational effort can be obtained as the step size is only refined when necessary. We first summarize the information that is needed for a variable step size BDF2 method in a way that is directly suitable for implementation in an existing code. We then propose a solution verification procedure that does not require direct control of the step size to carry out refinement studies and apply it to a textbook example. Finally, we explore the use of the variable step size BDF2 method for time integration of the NavierStokes equations in the CFD package

== Full document ==
<pdf>Media:Draft_Content_631961461p3348.pdf</pdf>

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 == Abstract ==
-Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local truncation error. Significant savings in computational effort can be obtained as the step size is only refined when necessary. We first summarize the information that is needed for a variable step size BDF2 method in a way that is directly suitable for implementation in an existing code. We then propose a solution verification procedure that does not require direct control of the step size to carry out refinement studies and apply it to a textbook example. Finally, we explore the use of the variable step size BDF2 method for time integration of the NavierStokes equations in the CFD package
+Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local truncation error. Significant savings in computational effort can be obtained as the step size is only refined when necessary. We first summarize the information that is needed for a variable step size BDF2 method in a way that is directly suitable for implementation in an existing code. We then propose a solution verification procedure that does not require direct control of the step size to carry out refinement studies and apply it to a textbook example. Finally, we explore the use of the variable step size BDF2 method for time integration of the NavierStokes equations in the CFD package REFRESCO and find plausible results for vortex shedding in the wake of a cylinder, but no major savings for this particular case.
 == Full document ==
 <pdf>Media:Draft_Content_631961461p3348.pdf</pdf>

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