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restart_import

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{  RESTART_IMPORT.PDE

 

  This example reads the TRANSFER file created by RESTART_EXPORT.PDE

  and resumes execution at the exported time.

 

}

 

TITLE "Sod's Shock Tube Problem - restart"

SELECT

 ngrid= 100

 regrid=off

 errlim=1e-4

 

VARIABLES

 rho(1)

 u(1)

 P(1)

 xm = move(x)

 

DEFINITIONS

 len = 1

 wid = 0.01

 gamma = 1.4

{ define a damping term to kill unwanted oscillations }

 eps =  0.001 ! 3e-4

{ Read in the file exported by restart_export.pde.

   Use the imported mesh and problem time. }

transfermeshtime( 'restart_export_01_6.dat', rho0,u0,p0)

 

INITIAL VALUES

 rho = rho0

 u = u0

 P = p0

 

EULERIAN EQUATIONS

{ equations are stated as appropriate to the Eulerian (lab) frame.

   FlexPDE will convert to Lagrangian form for moving mesh

  Since the equation is really in x only, we add dyy(.) terms with natural(.)=0

   on the sidewalls to impose uniformity across the fictitious y coordinate }

 rho:   dt(rho) + u*dx(rho) + rho*dx(u)  = dyy(rho) + eps*dxx(rho)

 u:   dt(u) + u*dx(u) + dx(P)/rho  = dyy(u) + eps*dxx(u)

 P:   dt(P) + u*dx(P) + gamma*P*dx(u)  = dyy(P) + eps*dxx(P)

 xm:  dt(xm) = u

 

BOUNDARIES

REGION 1

  { we must impose the same equivalence dt(xm)=u on the side boundaries

   as in the body equations: }

  START(0,0)   natural(u)=0  dt(xm)=u line to (len,0)

  value(xm)=len     value(u)=0   line to (len,wid)

   dt(xm)=u   natural(u)=0       line to (0,wid)

  value(xm)=0     value(u)=0   line to close

 

TIME 0 TO 0.375

 

MONITORS

for cycle=5

  grid(x,10*y)

  elevation(rho) from(0,wid/2) to (len,wid/2) range (0,1)

  elevation(u) from(0,wid/2) to (len,wid/2) range (0,1)

  elevation(P) from(0,wid/2) to (len,wid/2) range (0,1)

 

PLOTS

for t=0 by 0.02 to 0.143, 0.16 by 0.02 to 0.375

  grid(x,10*y)

  elevation(rho) from(0,wid/2) to (len,wid/2) range (0,1)

  elevation(u) from(0,wid/2) to (len,wid/2) range (0,1)

  elevation(P) from(0,wid/2) to (len,wid/2) range (0,1)

 

END

 


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