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subroutine int_force(itimestep,dt,ntotal,hsml,mass,vx,niac,rho,
& eta,pair_i,pair_j,dwdx,u,itype,x,t,c,p,dvxdt,tdsdt,dedt)
c----------------------------------------------------------------------
c Subroutine to calculate the internal forces on the right hand side
c of the Navier-Stokes equations, i.e. the pressure gradient and the
c gradient of the viscous stress tensor, used by the time integration.
c Moreover the entropy production due to viscous dissipation, tds/dt,
c and the change of internal energy per mass, de/dt, are calculated.
c itimestep: Current timestep number [in]
c dt : Time step [in]
c ntotal : Number of particles [in]
c hsml : Smoothing Length [in]
c mass : Particle masses [in]
c vx : Velocities of all particles [in]
c niac : Number of interaction pairs [in]
c rho : Density [in]
c eta : Dynamic viscosity [in]
c pair_i : List of first partner of interaction pair [in]
c pair_j : List of second partner of interaction pair [in]
c dwdx : Derivative of kernel with respect to x, y and z [in]
c itype : Type of particle (material types) [in]
c u : Particle internal energy [in]
c x : Particle coordinates [in]
c itype : Particle type [in]
c t : Particle temperature [in/out]
c c : Particle sound speed [out]
c p : Particle pressure [out]
c dvxdt : Acceleration with respect to x, y and z [out]
c tdsdt : Production of viscous entropy [out]
c dedt : Change of specific internal energy [out]
implicit none
include 'param.inc'
integer itimestep, ntotal,niac,pair_i(max_interaction),
& pair_j(max_interaction), itype(maxn)
double precision dt, hsml(maxn), mass(maxn), vx(dim,maxn),
& rho(maxn), eta(maxn), dwdx(dim,max_interaction), u(maxn),
& x(dim,maxn), t(maxn), c(maxn), p(maxn), dvxdt(dim,maxn),
& tdsdt(maxn),dedt(maxn)
integer i, j, k, d
double precision dvx(dim), txx(maxn), tyy(maxn),
& tzz(maxn), txy(maxn), txz(maxn), tyz(maxn), vcc(maxn),
& hxx, hyy, hzz, hxy, hxz, hyz, h, hvcc, he, rhoij
c Initialization of shear tensor, velocity divergence,
c viscous energy, internal energy, acceleration
do i=1,ntotal
txx(i) = 0.e0
tyy(i) = 0.e0
tzz(i) = 0.e0
txy(i) = 0.e0
txz(i) = 0.e0
tyz(i) = 0.e0
vcc(i) = 0.e0
tdsdt(i) = 0.e0
dedt(i) = 0.e0
do d=1,dim
dvxdt(d,i) = 0.e0
enddo
enddo
c Calculate SPH sum for shear tensor Tab = va,b + vb,a - 2/3 delta_ab vc,c
if (visc) then
do k=1,niac
i = pair_i(k)
j = pair_j(k)
do d=1,dim
dvx(d) = vx(d,j) - vx(d,i)
enddo
if (dim.eq.1) then
hxx = 2.e0*dvx(1)*dwdx(1,k)
else if (dim.eq.2) then
hxx = 2.e0*dvx(1)*dwdx(1,k) - dvx(2)*dwdx(2,k)
hxy = dvx(1)*dwdx(2,k) + dvx(2)*dwdx(1,k)
hyy = 2.e0*dvx(2)*dwdx(2,k) - dvx(1)*dwdx(1,k)
endif
hxx = 2.e0/3.e0*hxx
hyy = 2.e0/3.e0*hyy
hzz = 2.e0/3.e0*hzz
if (dim.eq.1) then
txx(i) = txx(i) + mass(j)*hxx/rho(j)
txx(j) = txx(j) + mass(i)*hxx/rho(i)
else if (dim.eq.2) then
txx(i) = txx(i) + mass(j)*hxx/rho(j)
txx(j) = txx(j) + mass(i)*hxx/rho(i)
txy(i) = txy(i) + mass(j)*hxy/rho(j)
txy(j) = txy(j) + mass(i)*hxy/rho(i)
tyy(i) = tyy(i) + mass(j)*hyy/rho(j)
tyy(j) = tyy(j) + mass(i)*hyy/rho(i)
endif
c Calculate SPH sum for vc,c = dvx/dx + dvy/dy + dvz/dz:
hvcc = 0.
do d=1,dim
hvcc = hvcc + dvx(d)*dwdx(d,k)
enddo
vcc(i) = vcc(i) + mass(j)*hvcc/rho(j)
vcc(j) = vcc(j) + mass(i)*hvcc/rho(i)
enddo
endif
do i=1,ntotal
c Viscous entropy Tds/dt = 1/2 eta/rho Tab Tab
if (visc) then
if (dim.eq.1) then
tdsdt(i) = txx(i)*txx(i)
else if (dim.eq.2) then
tdsdt(i) = txx(i)*txx(i) + 2.e0*txy(i)*txy(i)
& + tyy(i)*tyy(i)
endif
tdsdt(i) = 0.5e0*eta(i)/rho(i)*tdsdt(i)
endif
c Pressure from equation of state
if (abs(itype(i)).eq.1) then
call p_gas(rho(i), u(i), p(i),c(i))
else if (abs(itype(i)).eq.2) then
call p_art_water(rho(i), p(i), c(i))
endif
enddo
c Calculate SPH sum for pressure force -p,a/rho
c and viscous force (eta Tab),b/rho
c and the internal energy change de/dt due to -p/rho vc,c
do k=1,niac
i = pair_i(k)
j = pair_j(k)
he = 0.e0
c For SPH algorithm 1
rhoij = 1.e0/(rho(i)*rho(j))
if(pa_sph.eq.1) then
do d=1,dim
c Pressure part
h = -(p(i) + p(j))*dwdx(d,k)
he = he + (vx(d,j) - vx(d,i))*h
c Viscous force
if (visc) then
if (d.eq.1) then
c x-coordinate of acceleration
h = h + (eta(i)*txx(i) + eta(j)*txx(j))*dwdx(1,k)
if (dim.ge.2) then
h = h + (eta(i)*txy(i) + eta(j)*txy(j))*dwdx(2,k)
endif
endif
elseif (d.eq.2) then
c y-coordinate of acceleration
h = h + (eta(i)*txy(i) + eta(j)*txy(j))*dwdx(1,k)
& + (eta(i)*tyy(i) + eta(j)*tyy(j))*dwdx(2,k)
endif
! endif
h = h*rhoij
dvxdt(d,i) = dvxdt(d,i) + mass(j)*h
dvxdt(d,j) = dvxdt(d,j) - mass(i)*h
enddo
he = he*rhoij
dedt(i) = dedt(i) + mass(j)*he
dedt(j) = dedt(j) + mass(i)*he
c For SPH algorithm 2
c else if (pa_sph.eq.2) then
c do d=1,dim
c h = -(p(i)/rho(i)**2 + p(j)/rho(j)**2)*dwdx(d,k)
c he = he + (vx(d,j) - vx(d,i))*h
c Viscous force
if (visc) then
if (d.eq.1) then
c x-coordinate of acceleration
h = h + (eta(i)*txx(i)/rho(i)**2 +
& eta(j)*txx(j)/rho(j)**2)*dwdx(1,k)
if (dim.ge.2) then
h = h + (eta(i)*txy(i)/rho(i)**2 +
& eta(j)*txy(j)/rho(j)**2)*dwdx(2,k)
if (dim.eq.3) then
h = h + (eta(i)*txz(i)/rho(i)**2 +
& eta(j)*txz(j)/rho(j)**2)*dwdx(3,k)
endif
endif
elseif (d.eq.2) then
c y-coordinate of acceleration
h = h + (eta(i)*txy(i)/rho(i)**2
& + eta(j)*txy(j)/rho(j)**2)*dwdx(1,k)
& + (eta(i)*tyy(i)/rho(i)**2
& + eta(j)*tyy(j)/rho(j)**2)*dwdx(2,k)
endif
endif
dvxdt(d,i) = dvxdt(d,i) + mass(j)*h
dvxdt(d,j) = dvxdt(d,j) - mass(i)*h
c enddo
dedt(i) = dedt(i) + mass(j)*he
dedt(j) = dedt(j) + mass(i)*he
c endif
c enddo
c Change of specific internal energy de/dt = T ds/dt - p/rho vc,c:
do i=1,ntotal
dedt(i) = tdsdt(i) + 0.5e0*dedt(i)
enddo
end
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发表于 2020-9-23 01:28:24
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