Linear Advection Equation
Dear Users, Is there a way to solve a linear advection equation in nek5k without computing the Navier-Stokes equations? I am simply interested in advecting a profile according to the following: D(phi)/Dt = d (phi) /dt + v*.*grad(phi)= 0 where v*.*grad(phi) = u.d(phi)/dx + v.d(phi)/dy + w.d(phi)/dz and v is a prescribed velocity (for example v = (1,1) in 2D) Best, Saumil
Set ifflow to false and ifheat to T and ifadvc = F T F F F F... in the .rea file. Then, supply your velocity field in useric (ux, uy, uz), or, if you want time-varying velocity, do so in usrchk by over-writing the velocity field arrays, vx(), vy(), and vz() at each step. Paul ________________________________ From: [email protected] [[email protected]] on behalf of [email protected] [[email protected]] Sent: Saturday, February 28, 2015 9:24 AM To: [email protected] Subject: [Nek5000-users] Linear Advection Equation Dear Users, Is there a way to solve a linear advection equation in nek5k without computing the Navier-Stokes equations? I am simply interested in advecting a profile according to the following: D(phi)/Dt = d (phi) /dt + v.grad(phi)= 0 where v.grad(phi) = u.d(phi)/dx + v.d(phi)/dy + w.d(phi)/dz and v is a prescribed velocity (for example v = (1,1) in 2D) Best, Saumil
Thank You, Paul. Why does the conductivity/diffusivity (i.e. param(08)) have to be small and non-zero positive? Can nek5k solve the linear advection equation without the discrete diffusion term? On Sat, Feb 28, 2015 at 10:31 AM, <[email protected]> wrote:
Set ifflow to false and ifheat to T and ifadvc = F T F F F F...
in the .rea file.
Then, supply your velocity field in useric (ux, uy, uz), or, if you want time-varying velocity, do so in usrchk by over-writing the velocity field arrays, vx(), vy(), and vz() at each step.
Paul ------------------------------ *From:* [email protected] [ [email protected]] on behalf of [email protected] [[email protected]] *Sent:* Saturday, February 28, 2015 9:24 AM *To:* [email protected] *Subject:* [Nek5000-users] Linear Advection Equation
Dear Users,
Is there a way to solve a linear advection equation in nek5k without computing the Navier-Stokes equations? I am simply interested in advecting a profile according to the following:
D(phi)/Dt = d (phi) /dt + v*.*grad(phi)= 0
where v*.*grad(phi) = u.d(phi)/dx + v.d(phi)/dy + w.d(phi)/dz
and v is a prescribed velocity (for example v = (1,1) in 2D)
Best,
Saumil
_______________________________________________ Nek5000-users mailing list [email protected] https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
-- Saumil S. Patel Ph.D. Candidate Department of Mechanical Engineering Computational Multiphase Fluid Dynamics Group <https://sites.google.com/site/leeccny/> The City College of New York Telephone: 1 (212) 650-7134
Technically Nek solves convection-diffusion (CD). CD with nu=0 is invalid because it's a singular perturbation --- the number of boundary conditions is different for the 1st-order convection eqn than for the 2nd-order CD equation, so Nek checks to make certain nu \ge 0. I usually set nu=1.e-31.... it won't show up in the calculation (assuming your other quantities are O(1)). Best, Paul ________________________________ From: [email protected] [[email protected]] on behalf of [email protected] [[email protected]] Sent: Sunday, March 08, 2015 9:17 AM To: [email protected] Subject: Re: [Nek5000-users] Linear Advection Equation Thank You, Paul. Why does the conductivity/diffusivity (i.e. param(08)) have to be small and non-zero positive? Can nek5k solve the linear advection equation without the discrete diffusion term? On Sat, Feb 28, 2015 at 10:31 AM, <[email protected]<mailto:[email protected]>> wrote: Set ifflow to false and ifheat to T and ifadvc = F T F F F F... in the .rea file. Then, supply your velocity field in useric (ux, uy, uz), or, if you want time-varying velocity, do so in usrchk by over-writing the velocity field arrays, vx(), vy(), and vz() at each step. Paul ________________________________ From: [email protected]<mailto:[email protected]> [[email protected]<mailto:[email protected]>] on behalf of [email protected]<mailto:[email protected]> [[email protected]<mailto:[email protected]>] Sent: Saturday, February 28, 2015 9:24 AM To: [email protected]<mailto:[email protected]> Subject: [Nek5000-users] Linear Advection Equation Dear Users, Is there a way to solve a linear advection equation in nek5k without computing the Navier-Stokes equations? I am simply interested in advecting a profile according to the following: D(phi)/Dt = d (phi) /dt + v.grad(phi)= 0 where v.grad(phi) = u.d(phi)/dx + v.d(phi)/dy + w.d(phi)/dz and v is a prescribed velocity (for example v = (1,1) in 2D) Best, Saumil _______________________________________________ Nek5000-users mailing list [email protected]<mailto:[email protected]> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users -- Saumil S. Patel Ph.D. Candidate Department of Mechanical Engineering Computational Multiphase Fluid Dynamics Group<https://sites.google.com/site/leeccny/> The City College of New York Telephone: 1 (212) 650-7134
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