Hi Ben,
I use a constant time step of 0.05 sec with a backwards Euler implicit
time scheme. Of course, the local CFL increases to large numbers as the mesh is
refined, since I do not change the time step.
Do you typically change the time step post refinement? Or use local time
stepping?
The farfield boundary conditions I use are based on the Reimann
invariants, so I account for the components of flux coming in versus leaving
the flow domain via splitting the Jacobian. The solid wall boundary conditions
are enforced implicitly by modifying the flux at the wall through v \dot n = 0
(I am working with inviscid flow), and then I create a Jacobian for the
modified flux term. So, I don't think this could be an issue.
Jed: I am curious about your comment on lack of conservation of the GLS
schemes. I did a bit of search and came across the following two papers. They
make a case for conservation properties of the methods. I am curious what you
think.
Hughes, T. J. R., Engel, G., Mazzei, L., & Larson, M. G. (2000). The Continuous
Galerkin Method Is Locally Conservative. Journal of Computational Physics,
163(2), 467–488. doi:10.1006/jcph.2000.6577
Abstract: We examine the conservation law structure of the continuous Galerkin
method. We employ the scalar, advection–diffusion equation as a model problem
for this purpose, but our results are quite general and apply to
time-dependent, nonlinear systems as well. In addition to global conservation
laws, we establish local con- servation laws which pertain to subdomains
consisting of a union of elements as well as individual elements. These results
are somewhat surprising and contradict the widely held opinion that the
continuous Galerkin method is not locally conser- votive.
Hughes, T. J. R., & Wells, G. N. (2005). Conservation properties for the
Galerkin and stabilised forms of the advection–diffusion and incompressible
Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering,
194(9-11), 1141–1159. doi:10.1016/j.cma.2004.06.034
Abstract: A common criticism of continuous Galerkin finite element methods is
their perceived lack of conservation. This may in fact be true for
incompressible flows when advective, rather than conservative, weak forms are
employed. However, advective forms are often preferred on grounds of accuracy
despite violation of conservation. It is shown here that this deficiency can be
easily remedied, and conservative procedures for advective forms can be
developed from multiscale concepts. As a result, conservative stabilised finite
element procedures are presented for the advection–diffusion and incompressible
Navier–Stokes equations.
Manav
On Apr 18, 2013, at 7:25 AM, "Kirk, Benjamin (JSC-EG311)"
<[email protected]> wrote:
> On Apr 17, 2013, at 11:28 PM, "Manav Bhatia" <[email protected]> wrote:
>
>>> It's usually preferable to order your unknowns so that the fields are
>>> interlaced, with all values at a node contiguous.
>>
>> I will certainly give these a shot tomorrow. Do you know if these require
>> any other modification in my code/libMesh, or providing the command line
>> options would be enough?
>
> Jed's commas line option should work for older versions of libMesh, but if
> you are using 0.9.0 or newer the interlaced variables should be automatic if
> the DofMap properly discovers one "VariableGroup"
>
> What types of CFL numbers are you running at?
>
> My experience with compressible navier stokes (without mulrigrid) is that
> convergence is usually very good provided the numerical time step is less
> than the characteristic time of the flow (l_ref/U_ref). Going much higher
> than that for supersonic flows can give fits unless the boundary conditions
> are linearized perfectly. Given that the subsonic bcs are more complex I
> thought I'd mention this.
>
> -Ben
>
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