cinclude(ppm98_dfns.h) cinclude(ppm98_bdys.h) C C define(zero,ifelse(ifdouble,1,0.d+00,0.0e+00)) define(one,ifelse(ifdouble,1,1.d+00,1.0e+00)) define(two,ifelse(ifdouble,1,2.d+00,2.0e+00)) define(three,ifelse(ifdouble,1,3.d+00,3.0e+00)) define(four,ifelse(ifdouble,1,4.d+00,4.0e+00)) define(five,ifelse(ifdouble,1,5.d+00,5.0e+00)) define(six,ifelse(ifdouble,1,6.d+00,6.0e+00)) define(seven,ifelse(ifdouble,1,7.d+00,7.0e+00)) define(nine,ifelse(ifdouble,1,9.d+00,9.0e+00)) define(ten,ifelse(ifdouble,1,10.d+00,1.0e+01)) define(twelve,ifelse(ifdouble,1,12.d+00,1.2e+01)) define(ffteen,ifelse(ifdouble,1,15.d+00,1.5e+01)) define(onept1,ifelse(ifdouble,1,1.1d+00,1.1e+00)) define(point9,ifelse(ifdouble,1,.9d+00,9.0e-01)) define(half,ifelse(ifdouble,1,.5d+00,5.0e-01)) define(qtr,ifelse(ifdouble,1,.25d+00,2.5e-01)) define(eighth,ifelse(ifdouble,1,.125d+00,1.25e-01)) define(fifth,ifelse(ifdouble,1,.2d+00,2.0e-01)) define(tenth,ifelse(ifdouble,1,.1d+00,1.0e-01)) define(sxy4th,ifelse(ifdouble,1,.015625d+00,1.5625e-02)) c define(klein,ifelse(ifdouble,1,1.0d-08,1.0e-08)) subroutine ifelse(ifdouble,1,d_,)do_ppmlr_2d ^ ( xl, rho, p, u, e_total, ceul, rhonu, ^ e_totnu, unu, dt, smlrho, smallu, smalle, courmx, ^ n_real_zones_in, nbdy_set) c c ************************************************************************** c * THIS CODE IS DO_PPM_LR_1D. * c * THIS CODE WAS WRITTEN BY: WOODWARD RESEARCH GROUP. (c) 1998 * c * ALL RIGHTS RESERVED. VOID WERE PROHIBITED * c ************************************************************************** c c C WHAT This routine performs a 1D hydrodynamic calculation c performed as a Lagrangian step followed by a remap c step, with artificial diffusion. c c ASSUMPTIONS A Cartesian grid is assumed, which need not be uniform c A general (metal) equation of state is used: C p(i) = p00(i) + gamma1(i) * rho(i) * ei(i) c c c p = p00 + gamma1 * rho * ei c This implies that: c ce**2 = gamma1 * (ei + p / rho) c hence: c ce**2 = ((1 + gamma1) * p - p00 ) / rho c Note that the input data should be consistant with the c relation: c ce**2 = dpdrho + ddpdei c c and of course dpdrho must be positive and ddpdei c nonnegative. However, it is not necessary that the c pressure be positive. c C C BOUNDARIES The necessary number of boundary zones to set (NBDY_SET) c is 9, (three for interpolation, one for integration) times c two (lag and remap step), and diffuse takes one. It will c be further assumed that at the outset the 2*NBDY_SET c boundary zones [often referred to as fake zones] contain c valid values appropriate to the user's chosen boundary c conditions. C This is the only means of signalling boundary conditions C to this routine The user signals his understanding and c acknowledges this by passing to Do_PPM_LR_1D c the number of boundary zones set on each side. This c routine verifies that sufficient fake zones have been c provided before continuing. If not, an advisory is c displayed and the program terminated. C C DIMENSIONS c input It will be assumed that the dimensions of all zone-averaged c type quantities { e.g. RHO, P, U, RHONU, PNU, etc, ] are C [1-NBDY_SET:N_REAL_ZONES_IN+NBDY_SET]. C The dimensions of all [and I mean ALL] interface type C quantities [e.g. xl, dvoll, dmassl, pavl, uavl, anything C referenced to and interface, usually the lefthand zone c interface] are C [1-NBDY_SET:N_REAL_ZONES_IN+NBDY_SET+1]. C Note the "+1" please. There may be a quiz later. C C output At the completion of this entire routine, new zone-averaged C quantities [e.g. rhonu, pnu, unu] will have updated values C on the range C [1:N_REAL_ZONES_IN], C and any returned interface type thingies will have valid C values on the range [There are none at this time]: C [1:N_REAL_ZONES_IN+1]. c C c C DATA C input Input arrays are: C C xl: the locations of the lefthand zone interfaces, c defining the computational grid. Please realize c that a numerical grid of n zones would require n+1 xl c values (interface locations.) C rho: The zone-averaged densities C p: The zone-averaged pressures C u: The zone-averaged velocities C e_total: the zone-averaged total energy C ceul: A zone-averaged eulerian sound speed c c A general (metal) equation of state is used: C p(i) = p00(i) + gamma1(i) * rho(i) * ei(i) c p = p00 + gamma1 * rho * ei c This implies that: c ce**2 = gamma1 * (ei + p / rho) c hence: c ce**2 = ((1 + gamma1) * p - p00 ) / rho c Note that the input data should be consistant with the c relation: c ce**2 = dpdrho + ddpdei c c and of course dpdrho must be positive and ddpdei c nonnegative. However, it is not necessary that the c pressure be positive. c c c C Input scalers are: C C dt: the timestep. C smlrho: a trivial value for density C smallu: a trivial value for velocity C smalle: a trivial value for nergy C the above 4 values are generally about C 1.0e-06 for single precision and C 1.0d-08 for dourble precision. C n_real_zones_in: The number zones (NOT counting fake zones) to be c processed. Upon completion of the timestep, c this many zones will have valid entries in the c output arrays. C nbdy_set: Number of boundary zones on either end set. This c is a check to ensure sufficient values have been c set by the calling routine. The number of c boundary zones required on either side must be c at least equat to the required values: 9 C C output Output arrays are: C rhonu: The new zone-averaged densities at the new c timestep. C e_totnu: The new zone-averaged total energies at the new c timestep. C unu: The new zone-averaged velocities at the new c timestep. C C Output scaler is: C C courmx: The maximum Courant number found by this call C to this subroutine. C C c C C VORSICHT HABEN! C C IT IS ASSUMED THAT APPROPRIATE VALUES OF THE DEPENDENT QUANTITIES C (xl, rho, p ,u) HAVE BEEN PLACED INTO THESE BOUNDARY ZONES C BY THE CALLING ROUTINE TO IMPLIMENT WHATEVER BOUNDARY CONDITIONS C THE USER DESIRED. C C VORSICHT HABEN! C C ALL, REPEAT _*ALL*_ (n_real_zones_in + 2*nbdy_set) C ZONES OF RHO, P, U, and (n_real_zones_in + 2**nbdy_set+1) C ZONES OF XL (note the +1) WILL BE USED AND MUST CONTAIN C VALID VALUES. C C VORSICHT HABEN! C C The user signals his understanding and acknowledges this by C passing to Do_PPM_LR0_1Dthe number of boundary zones C set on each side. Ve haf vays of checking dis. C C C C************************************************************************* C************************************************************************* C************************************************************************* C************************************************************************* C************************************************************************* C ifelse(ifdouble,1,implicit real*8 (a-h,o-z), ) dimension xl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ rho(1-nbdy_set:n_real_zones_in + nbdy_set), ^ p(1-nbdy_set:n_real_zones_in + nbdy_set), ^ u(1-nbdy_set:n_real_zones_in + nbdy_set), ^ e_total(1-nbdy_set:n_real_zones_in + nbdy_set), ^ ceul(1-nbdy_set:n_real_zones_in + nbdy_set), ^ rhonu(1-nbdy_set:n_real_zones_in + nbdy_set), ^ e_totnu(1-nbdy_set:n_real_zones_in + nbdy_set), ^ unu(1-nbdy_set:n_real_zones_in + nbdy_set) character*100 msg allocatable :: gamma1(:), p00(:) allocatable :: courno(:), difuse_vel(:), ^ unsmad(:), unsmup(:), ^ stpadb(:), ^ rhoavl(:), pavl(:), ^ uavl(:), ^ dx(:), ^ dxinv(:), difusl(:), ^ dmassl(:), dmoml(:) allocatable :: denl(:) allocatable :: xllag(:), rholag(:), ^ plag(:), ulag(:), ^ e_totlag(:), dxlag(:) allocatable :: dmasll(:), dmasrl(:), ^ detotl(:), dm(:), ^ dmnu(:), dmnew(:) allocatable :: dvol(:), dvoll(:) allocatable :: dvolinv(:), dminv(:) allocatable :: dvolfl(:) allocatable :: ^ dmassfl(:), ^ dalfac(:), darfac(:), facda(:), fcdazl(:), ^ facdal(:), fa6dal(:), fa6dar(:), frrdal(:), ^ frrdar(:), flldal(:), flldar(:) small = klein c c We will create and use the following "K" indices as pointers to c the beginning and end of the working array. A count KDO will c also be maintained of the number of zones in the array to c process. Note that all of these shall refer to ZONE counts. c Quantities which depend upon lefthand zone interfaces, will c of course require one additional reference on the right. c the K*1's are appropriate whenever starting from scratch with c interpolation. KSTART1 = 1-NBDY_SET KEND1 = N_REAL_ZONES_IN + NBDY_SET KDO1 = N_REAL_ZONES_IN + 2 * NBDY_SET c print *,' KEND1 = N_REAL_ZONES_IN,NBDY_SET=',N_REAL_ZONES_IN,NBDY_SET c print *,' KEND1 = KSTART1,KEND1,KDO1=',KSTART1,KEND1,KDO1 courmx = 0.0 n_required = 9 if ( nbdy_set .lt. n_required ) then call ppm98_message( ' Do_PPM_LR_1D Error. ***',0) call ppm98_message( ^ ' Note. the number of boundary zones set at either end of the ',0) call ppm98_message( ^ ' computational grid do not match the required number.',0) call ppm98_message( ^ ' This routine which performes a single step of a Lagrangian+Remap',0) call ppm98_message( ^ ' hydrodynamic update (including artificial diffusion) requires',0) write(msg,6666) n_required call ppm98_message( msg,0) 6666 format(1x, i3,' fake zones at each end of the array') call ppm98_message( ^ ' IT IS ASSUMED THAT APPROPRIATE VALUES OF THE DEPENDENT',0) call ppm98_message( ^ ' QUANTITIS (xl, rho, p ,u) HAVE BEEN PLACED INTO THESE',0) call ppm98_message( ^ ' BOUNDARY ZONES BY THE CALLING ROUTINE TO IMPLIMENT ',0) call ppm98_message( ^ ' WHATEVER BOUNDARY CONDITIONS THE USER DESIRED. ALL',0) call ppm98_message( ^ ' (n_real_zones_in + 2*nbdy_set)',0) call ppm98_message( ^ ' ZONES OF RHO, P, U and ',0) call ppm98_message( ^ ' (n_real_zones_in + 2*nbdy_set+1)',0) call ppm98_message( ^ ' ZONES OF XL (note the +1) WILL BE USED AND MUST ',0) call ppm98_message( ^ ' CONTAIN VALID VALUES.',0) write(msg,6667) nbdy_set,n_required call ppm98_message( msg,0) 6667 format(' The calling program passed',i6,' boundary zones but ',i3, ' zones') write(msg,6668) n call ppm98_message( msg,-1) 6668 format(' are required. There were ',i9,' non-boundary zones passed.') stop endif allocate ( ^ p00(1-nbdy_set:n_real_zones_in + nbdy_set), ^ gamma1(1-nbdy_set:n_real_zones_in + nbdy_set)) allocate ( ^ courno(1-nbdy_set:n_real_zones_in + nbdy_set), ^ detotl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ difuse_vel(1-nbdy_set:n_real_zones_in + nbdy_set), ^ difusl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dm(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dmasll(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dmasrl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dmassl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dminv(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dmnew(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dmnu(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dmoml(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ denl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dvol(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dvolinv(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dvoll(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dvolfl(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dmassfl(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dx(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dalfac(1-nbdy_set:n_real_zones_in + nbdy_set), ^ darfac(1-nbdy_set:n_real_zones_in + nbdy_set), ^ facda(1-nbdy_set:n_real_zones_in + nbdy_set), ^ fcdazl(1-nbdy_set:n_real_zones_in + nbdy_set), ^ facdal(1-nbdy_set:n_real_zones_in + nbdy_set), ^ fa6dal(1-nbdy_set:n_real_zones_in + nbdy_set), ^ fa6dar(1-nbdy_set:n_real_zones_in + nbdy_set), ^ frrdal(1-nbdy_set:n_real_zones_in + nbdy_set), ^ frrdar(1-nbdy_set:n_real_zones_in + nbdy_set), ^ flldal(1-nbdy_set:n_real_zones_in + nbdy_set), ^ flldar(1-nbdy_set:n_real_zones_in + nbdy_set), ^ dxinv(1-nbdy_set:n_real_zones_in + nbdy_set), ^ rhoavl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ stpadb(1-nbdy_set:n_real_zones_in + nbdy_set), ^ pavl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ uavl(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ unsmad(1-nbdy_set:n_real_zones_in + nbdy_set), ^ unsmup(1-nbdy_set:n_real_zones_in + nbdy_set) ^ ) allocate ( ^ xllag(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ dxlag(1-nbdy_set:n_real_zones_in + nbdy_set+1), ^ rholag(1-nbdy_set:n_real_zones_in + nbdy_set), ^ plag(1-nbdy_set:n_real_zones_in + nbdy_set), ^ ulag(1-nbdy_set:n_real_zones_in + nbdy_set), ^ e_totlag(1-nbdy_set:n_real_zones_in + nbdy_set)) c c c note that ALL interface thingies are dimensioned one more. c c c compute some essential quantities: c do i=kstart1, kend1 dx(i) = xl(I+1) - xl(i) dxinv(i) = 1.0 / dx(i) dvol(i) = dx(i) dvolinv(i) = dxinv(i) c NOTE these last two are true only in cartesian coords. dm(i) = rho(i) * dvol(i) dminv(i) = 1.0 / dm(i) cesq = ceul(i) * ceul(i) ek = 0.5 * ( u(i)*u(i) ) ei = e_total(i) - ek gamma1(i) = cesq / (ei + p(i)/rho(i) ) p00(i) = p(i) - gamma1(i) * rho(i) * ei enddo c c Precompute various geometrical factors for use when interpolating c on a non-uniform grid. This permits greater efficiencies when c several quantities are to be interpolated. c c nbdy = 3 c nbdy_set should be <= NBDY_SET ! K = KSTART1 nzones = KDO1 - 2*nbdy c c precompute the interpolation factors call ifelse(ifdouble,1,d_,) ppm98_interpolation_factors ^ ( dx(K), dalfac(K), darfac(K), facda(K), fcdazl(K), ^ facdal(K), fa6dal(K), fa6dar(K), frrdal(K), frrdar(K), ^ flldal(K), flldar(K), nzones,nbdy) c Get the fluxes of the conserved hydrodynamical quantities: c These are mass, longitudinal momentum, and energy. c do_ppm98_lag_flux requires 4 fake zones on each end of grid c c c DO_PPM98_LAG_FLUX produces the Lagrangian zone interface fluxes in the c longitudinal direction (the direction of this pass) for the c conserved hydrodynamic quantities mass, longitudinal momentum c and total energy in the following steps: c c 1) Interpolate, with monotonicity constraints the c pressure and longitudinal velocity by constructing c interpolations of the +- Riemann invarients. c (Returns UNSMUP) c 2) Using these piecewise parabolic interpolations for c , velocity and pressure, find the c averages in the appropriate domains of dependence c for a Riemann problem at each zone interface. c 3) Solve Riemann shock tube problems at each lefthand c zone interface to obtain appropriate time-averaged c values for pressure, and longitudinal velocity at c these interfaces. Time averages of density are not c required for a Lagrangian calculation. c (Returns PAVL, UAVL.) c 4) Determine the Courant condition (stability) for c each _INTERFACE_. Simply put, in order for c the method to be stable, the various Domains c of dependence for the Riemann problems c cannont exceed the width of either the zone c to the left or the zone to the right. This c make the courant number array COURNO appear c to be an interface-like quantity. Its valid c range shall be [K:K+NZONES] c c These individual steps are also available as separate c modules. c nbdy = 4 K = KSTART1 NZONES = KDO1 -2*nbdy c NZONES is the count of the number of zones which will have valid c entries in the output from DO_PPM98_LAG_FLUX_GAMMA c call ifelse(ifdouble,1,d_,)do_ppm98_lag_flux ^ ( xl(K), dx(K), ^ dalfac(K), darfac(K), facda(K), fcdazl(K), facdal(K), fa6dal(K), ^ fa6dar(K), flldal(K), flldar(K), frrdal(K), frrdar(K), ^ rho(K), p(K), u(K), ceul(K), p00(K), ^ gamma1(K), unsmup(K), ^ pavl(K), uavl(K), courno(K), ^ dt, nzones, nbdy) c update the zone counts. These are the valid counts for the interface c fluxes, dmassl, dvoll, etc. The number of these boundary fluxes which c are for zone THIS program considers fake are (beginning #) - (used #) c This program began with nbdy_set, and nbdy were just used. c nbdy_hydroflux is the number of fake zones with fluxes. nbdy_hydroflux = nbdy_set - nbdy KSTART2 = KSTART1 + nbdy KEND2 = KEND1 - nbdy KDO2 = KDO1 - 2*nbdy c c Thus the fluxes are now valid on the range (kstart2,kend2. To examine c them one could do: c print *,' i, pavl(i), uavl(i)' c do i=kstart2,kend2+1 c write(6,666) i, pavl(i), uavl(i) c enddo 666 format(1h ,i4,1p,9(1x,e10.3)) 66 format(1h ,i4,1p,9(1x,e10.3)) c the K*2 will be appropriate for working with fluxes (before diffuse) c find the courant number from the above step. When a routine is c called with an array such as COURNO, the old values of COURNO are c overwritten. Thus the Courant number should be determined after each c such routine, or different arrays used. c c To be stable when a flux at xl(i), the left hand edge of zone I, is c computed, the courant numbers in zone I-1 and I need to be <= 1.0 c Thus we examine Courant numbers over the KSTART2-1,KEND2+1 c courmxh = courno(KSTART2 -1) do i=KSTART2 , KEND2+1 courmxh = max (courmxh, courno(i)) enddo c c c c c PPM98_LAG_UPDATE_CART upates the zone averages by conserviatvely c differencing the fluxes found above, assuming cartesian c coordinates and no body forces. Body forces would c entail and additional term added to the new zone-averages of c velocity and total energy AFTER this routine is called. c c The suffix "lag" will be appended to the updated quantities C (XLLAG, DXLAG, RHOLAG, ULAG, E_TITLAG) to indicate that these c are the quantities after the lagrangian step. (DMLAG == DM of c course) Traditional, quantities were renamed at this point, c over writing the initial data. This is now avoided, as well as c the gratuitous copying. c K = KSTART2 nzones = KDO2 call ifelse(ifdouble,1,d_,)ppm98_lag_update_cart ^ ( xl(K), dx(K), dm(K), u(K), ^ e_total(K), uavl(K), pavl(K), xllag(k), dxlag(K), ^ rholag(K), ulag(K), 6 e_totlag(K), smallu, smalle, dt, nzones) c no fake zones necessary in the above routine, so the "K" count is c unchanged. The updated zone-averages are valid on the range c kstart2,kend2, and could be examined by: c c print *,' Finished with the lag step.' c print *,' i, xllag(i), rholag(i), ulag(i), e_totlag(i), plag(i)' do i=kstart2,kend2 ekk = 0.5 * (ulag(i)**2) eii = e_totlag(i) - ekk plag(i) = (gamma1(i)) * rholag(i)*eii c write(6,666) i,xllag(i), rholag(i), ulag(i), e_totlag(i), plag(i) enddo C ********************************************************** C * * C * Done with the Lagrangian step, begin remap step * C * * C ********************************************************** C c The grid is now definitely non uniform. So, first pre compute c the geometrical factors (the old factors are destroyed) nbdy = 3 c nbdy_set should be <= NBDY_SET ! K = kstart2 nzones = KDO2 - 2*nbdy c c precompute the interpolation factors call ifelse(ifdouble,1,d_,) ppm98_interpolation_factors ^ (dxlag(K), dalfac(K), darfac(K), facda(K), fcdazl(K), ^ facdal(K), fa6dal(K), fa6dar(K), frrdal(K), frrdar(K), ^ flldal(K), flldar(K), nzones,nbdy) c c Get the advection fluxes nbdy = 4 k=kstart2 nzones = kdo2-2*nbdy C call ifelse(ifdouble,1,d_,,) ppm98_map_flux_2d ^ ( dalfac(K), darfac(K), facda(K), fcdazl(K), facdal(K), fa6dal(K), ^ fa6dar(K), flldal(K), flldar(K), frrdal(K), frrdar(K), ^ xllag(k), xl(K), rholag(k), plag(k), ulag(k), ^ ceul(k), p00(k), gamma1(k), ^ unsmad(k), unsmup(k), stpadb(k), dvoll(k), ^ dmassl(k), dmoml(k), denl(k), dvolfl(k), dmassfl(k), 6 courno(k), dt, smalle, nzones, nbdy) kstart3=kstart2+nbdy kend3=kend2-nbdy kdo3 = kdo2-2*nbdy c find the courant number from the above step. When a routine is c called with an array such as COURNO, the old values of COURNO are c overwritten. Thus the Courant number should be determined after each c such routine, or different arrays used. c c To be stable when a flux at xl(i), the left hand edge of zone I, is c computed, the courant numbers in zone I-1 and I need to be <= 1.0 c Thus we examine Courant numbers over the KSTART3-1,KEND3+1 c courmxa = courno(KSTART3 -1) do i=KSTART3 , KEND3+1 courmxa = max (courmxa, courno(i)) enddo c c These can be examined by c c print *,' i,rholag(i), dvoll(i), dmassl(i), dmoml(i), denl(i)' c do i=kstart3,kend3+1 c write(6,66) i,rholag(i), dvoll(i), dmassl(i), dmoml(i), denl(i) c enddo c c New update the zone averages by conservatively differencing these c fluxes. c c print *,' i,rhonu(i), unu(i), e_totnu(i)' do i=kstart3,kend3 dmnu(i) = dm(i) + dmassl(i)- dmassl(i+1) rhonu(i) = dmnu(i) * dxinv(i) unu(i) = (ulag(i)*dm(i) + dmoml(i)-dmoml(i+1))/dmnu(i) eenew = (e_totlag(i)*dm(i) + denl(i)-denl(i+1))/dmnu(i) eknew = 0.5*unu(i)*unu(i) einew = max (smalle, eenew - eknew) e_totnu(i) = einew+eknew c write(6,66) i,rhonu(i), unu(i), e_totnu(i) enddo c c Due to the mixing of gasses from different zones, the EOS is c no longer known, thus the new pressures cannot be determined c here. That requires a reference to the actual equation of c state. c c C ********************************************************** C * * C * Done with the hydro step, begin diffusion step * C * * C ********************************************************** c zone centerred difusion velocities are required on the range c zone zone just updated. Any bondary requirements (offsets) c are built in into the offsets in the calling statement. c c Therefore the correct relative beginning locations is KSTART2 c and the number of zone to process is KDO2 c c BUT REALIZE THAT PPM98_EUL_DIFFUSE_1D OPERATES ON THE INITIAL C DATA. c c c KSTARTDF = KSTART3 KENDDF = KEND3 KDODF = KDO3 c c c Get difusion velocities c c PPM98_DIFUSE0_1D obtains zone centered Eulerian diffusion velocities. c (It's like sausage, you don't really want to know it's done) c K=KSTARTDF nzones = KDODF c call ifelse(ifdouble,1,d_,) ppm98_eul_difuse_2d c ^ ( dx(k-2), dx(k-1), dx(K), dx(k+1), dx(k+2), c ^ u(k-2), u(k-1), u(K), u(k+1), u(k+2), c ^ p(k-2), p(K), p(k+2), rho(k-2), rho(K), rho(k+2), c ^ ceul(k-2), ceul(K), ceul(k+2), c ^ difuse_vel(K), smallu, nzones) c update the zone counts KSTARTDF1 = KSTARTDF KENDDF1 = KENDDF KDODF1 = KDODF courdf1 = courno(KSTARTDF1) do i=KSTARTDF1+1,KENDDF1 courdf1 = max (courdf1,courno(i)) enddo c At this point, we should have one extra difuseion velocity c at each end of the working arry. These are ZONE-CENTERED c velocities, from which INTERFACE centerred fluxes will c be constructed. This construction requires this extra fake zone. C Now apply diffusion c c First get the diffusive zone interface fluxes c from the zone centerred difusion velocities nbdy_difuse_fluxes = 1 K = KSTARTDF1 nzones = KDODF1 - 2*nbdy_difuse_fluxes call ifelse(ifdouble,1,d_,) ppm98_difuseflux_hydro_cart ^ ( dx(K), difuse_vel(K), ^ rhonu(K), unu(K), e_totnu(K), ^ dvoll(K), dmasll(K), dmasrl(K), ^ dmassl(K), dmoml(K), detotl(K), ^ courno(K), dt, nzones, ^ nbdy_difuse_fluxes ) KSTARTDF2 = KSTARTDF1 + nbdy_difuse_fluxes KENDDF2 = KENDDF1 - nbdy_difuse_fluxes courdf2 = courno(KSTARTDF2) do i=KSTARTDF2+1,KENDDF2 courdf2 = max (courdf2,courno(i)) enddo c Now, apply the diffusive fluxes c c (Final update:, whew!) c c We occasionally get underflows by allowing absurdly small c velocities to be computed. Therefore, we will set such c velocities to zero below. c ssmalu = small * smallu ssmlu2 = ssmalu * ssmalu c c print *,' i, rhonu(i), unu(i), e_totnu(i), pnu(i)' do 9100 i = KSTARTDF2,KENDDF2 c dmnew(i) = dmnu(i) c this saves a flop or two: if ((dvoll(i) + dvoll(i+1)) .ne. zero) then c dmnew(i) = rhonu(i) * dvol(I) dmnu(i) = dmnew(i) + dmassl(i) - dmassl(i+1) rhonu(i) = dmnu(i) * dvolinv(i) dmnui = one / dmnu(i) unu(i) = (unu(i) * dmnew(i) + dmoml(i) - dmoml(i+1)) * dmnui e_totnu(i) = (e_totnu(i) * dmnew(i) + ^ detotl(i) - detotl(i+1)) * dmnui 9099 continue endif usq = unu(i) * unu(i) c if ((unu(i) * unu(i)) .lt. ssmlu2) unu(i) = 0.0 if ( usq .lt. ssmlu2) then unu(i) = 0.0 usq = 0.0 endif c write(6,666) i, rhonu(i), unu(i), e_totnu(i) 9100 continue c c The final Courant number is the maximum of the c hydrodynamics advective, and diffusive Courant numbers. c courmx = max (courmxh, courmxa, courdf1, courdf2 ) deallocate (courno, difuse_vel) deallocate ( unsmad, unsmup, stpadb ) deallocate ( rhoavl, pavl, uavl) deallocate ( dx, dxinv) deallocate ( difusl, dmassl, denl, dmoml, detotl) deallocate ( dmasll, dmasrl) deallocate (dvolfl) c deallocate (denl, dmassfl) deallocate (dvol, dvoll) deallocate (dm, dmnu, dmnew ) deallocate (dvolinv, dminv) c c return end