[petsc-users] petsc-users Digest, Vol 26, Issue 30

[Kontsantinos Kontzialis]

On 02/13/2011 08:00 PM, petsc-users-request at mcs.anl.gov wrote:
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> Today's Topics:
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>     1. Re:  Guidelines for solving the euler equations with an
>        implicit matrix free approach (Matthew Knepley)
>     2.  Reading vtk file in parallel and assigning to an array
>        (khalid ashraf)
>     3. Re:  Reading vtk file in parallel and assigning to an	array
>        (Matthew Knepley)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sat, 12 Feb 2011 16:12:36 -0600
> From: Matthew Knepley<knepley at gmail.com>
> Subject: Re: [petsc-users] Guidelines for solving the euler equations
> 	with an implicit matrix free approach
> To: PETSc users list<petsc-users at mcs.anl.gov>
> Message-ID:
> 	<AANLkTimus8N2jUu7Bvu0TZe59dr4FTpoJFh+m0QQUN-V at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> On Fri, Feb 11, 2011 at 10:37 AM, Kontsantinos Kontzialis<
> ckontzialis at lycos.com>  wrote:
>
>> Dear Petsc team,
>>
>>   I'm new in Petsc and I'm trying to solve the euler equations of fluid
>> dynamics
>> using an implicit matrix free approach with a spatial discontinues galerkin
>> discretization.
>> I need some directions about how can I solve the following system:
>>
>> (M/dt+dR/du)*DU=R
>>
>> where R denotes the residual of the system and dR/du the residual jacobian.
>> Please help.
>>
> Petsc provides linear algebra and nonlinear solvers. This is fine once you
> have discretized.
> It sounds like you will use DG:
>
>    a) on a structured or unstructured grid?
>
> The PETSc DA supports structured grids in any dimension. After this, you
> want to use the
> TS object to present your system. There are many examples in the TS, e.g.
> ex10 for
> radiation-diffusion or ex14 for hydrostatic ice flow.
>
> Once you have your problem producing the correct residual and Jacobian, we
> can talk
> about solvers.
>
>     Matt
>
>
>> Kostas
>>
Mat,

Thank you for your reply. I have done the discretization and the 
residual and jacobian are computes correctly. Furthermore, I managed to 
do some calculation using TS but with an explicit scheme. I need to work 
with an implicit time discretization and I have read in a quite few 
papers that they follow the matrix free approach.

Thank you,

Kostas