see the USER-SPH user's guide for a detailed explanation of these examples.

dimension          2

units              si

atom_style         meso

# create simulation box

region             box block -0.050e-3 1.044e-3 -0.05e-3 1.044e-3 -1.0e-6 1.0e-6 units box

create_box         3 box

# create fluid particles

region             fluid block 0.0001e-3 0.999e-3 0.0001e-3 0.999e-3 EDGE EDGE side in units box 

lattice            sq 0.025e-3

create_atoms       1 region fluid

# create bottom, left, and right wall

region             walls block 0.0001e-3 0.999e-3 0.0001e-3 EDGE EDGE EDGE side out units box 

lattice            sq2 0.025e-3

create_atoms       2 region walls

# create a driver strip of particles, which exerts shear forces on the fluid

region             driver block EDGE EDGE 0.999e-3 EDGE EDGE EDGE side in units box 

create_atoms       3 region driver

group              fluid type 1 

group              walls type 2 

group              driver type 3

group              integrate_full union fluid driver

mass               3 2.0e-7

mass               2 2.0e-7

mass               1 4.0e-7

set                group all meso_rho 1000.0

# use Tait's EOS in combination with Morris' laminar viscosity.

# We set rho_0 = 1000 kg/m^3, c = 0.1 m/s, h = 6.5e-5 m.

# The dynamic viscosity is set to 1.0e-3 Pa s, corresponding to a kinematic viscosity of 1.0e-6 m^2/s

pair_style         hybrid sph/taitwater/morris

pair_coeff         * *    sph/taitwater/morris 1000 0.1 1.0e-3 6.5e-5

pair_coeff         2 3    none # exclude interaction between walls and shear driver

compute            rho_peratom all meso_rho/atom

compute            e_peratom all meso_e/atom

compute            ke_peratom all ke/atom

compute            esph all reduce sum c_e_peratom

compute            ke all ke

variable           etot equal c_ke+c_esph

# assign a constant velocity to shear driver

velocity           driver set 0.001 0.0 0.0 units box

fix                freeze_fix driver setforce 0.0 0.0 0.0

# do full time integration for shear driver and fluid, but keep walls stationary

fix                integrate_fix_full integrate_full meso

fix                integrate_fix_stationary walls meso/stationary

dump               dump_id all custom 100 dump.lammpstrj id type xs ys zs vx vy c_rho_peratom c_e_peratom

dump_modify        dump_id first yes

thermo             100

thermo_style       custom step c_esph v_etot

thermo_modify      norm no

neighbor           3.0e-6 bin

timestep           5.0e-5

run                4000

#!/usr/bin/gnuplot

# compare sph/heatconduction output with analytic solution to diffusion equation

alpha = 1.0e-4

time = 4.0

analytic_profile(x) = 1.5 + 0.5*erf((x-49.5e-2)/sqrt(4.0*alpha*time))

set ylabel "internal energy per particle"

set xlabel "x position [m]"

plot [][0.5:2.5]'dump.last' u 3:6 ti "SPH simulation", analytic_profile(x) ti "analytic solution"

pause -1

#set terminal postscript color enhanced lw 2

#set out "heat_profile.ps"

set table "simu.dat"

plot [0:1][0.5:2.5]'dump.last' u 3:6

set table "analytic.dat"

set samples 1000

plot [0:1][0.5:2.5] analytic_profile(x)

#replot

# mesoscopic heat conduction

# heat flow from hot right region to cold left region

# compare the temperature profile at the end opf the simulation,

# contained in file dump.last, to analytic solution.

#

#

dimension       2

units		si

atom_style	meso

boundary        f p p

lattice		sq 0.01

region		box block 0 100 0 10 0 0.1 

create_box	1 box

create_atoms	1 box

mass            1 1.0e-5

region          left  block EDGE 49.9  EDGE EDGE EDGE EDGE

region          right block 50 EDGE EDGE EDGE EDGE EDGE

set             region left  meso_e 1.0 # internal energies

set             region right meso_e 2.0

set             group all meso_rho 0.1 # mesoscopic density is also needed for this pair style

#               For correct temperature profiles, mescoscopic density and mass * number density must coincide!

pair_style      sph/heatconduction

#               i j diffusion coeff. cutoff

pair_coeff      1 1 1.0e-4           2.0e-2

compute         ie_atom all meso_e/atom

compute         ie all reduce sum c_ie_atom

thermo		10

thermo_style    custom step temp c_ie

timestep        0.25e-1

neighbor	0.2e-2 bin

fix             integrate_fix all meso/stationary

dump		dump_fix all custom 10 dump.heat id type x y z c_ie_atom

dump_modify     dump_fix first yes

run             160

undump          dump_fix

dump		dump_fix all custom 10 dump.last id type x y z c_ie_atom

dump_modify     dump_fix first yes

run             0

undump          dump_fix

dump		dump_fix all custom 10 dump.last.xs id type xs ys zs c_ie_atom

dump_modify     dump_fix first yes

run             0

undump          dump_fix

# mesoscopic heat conduction

# heat flow from hot right region to cold left region

# compare the temperature profile at the end opf the simulation,

# contained in file dump.last, to analytic solution.

#

#

units		si

atom_style	meso

newton          on

boundary        f p p

lattice		sc 0.01

region		box block 0 100 0 10 0 10 

create_box	1 box

create_atoms	1 box

mass            1 1.0e-5

region          left  block EDGE 49.9  EDGE EDGE EDGE EDGE

region          right block 50 EDGE EDGE EDGE EDGE EDGE

set             region left  meso_e 1.0 # internal energies

set             region right meso_e 2.0

set             group all meso_rho 10.0 # mesoscopic density is also needed for this pair style

#               For correct temperature profiles, mescoscopic density and mass * number density must coincide!

pair_style      sph/heatconduction

#               i j diffusion coeff. cutoff

pair_coeff      1 1 1.0e-4           2.0e-2

neighbor	0.2e-2 bin

neigh_modify	every 20 delay 0 check no

compute         ie_atom all meso_e/atom

compute         ie all reduce sum c_ie_atom

thermo_style    custom step temp c_ie

thermo_modify   norm no

fix             integrate_fix all meso/stationary

thermo		10

timestep        0.25e-1

dump		dump_fix all custom 10 dump.heat id type x y z c_ie_atom

dump_modify     dump_fix first yes

run             160

undump          dump_fix

dump		dump_fix all custom 10 dump.last id type x y z c_ie_atom

dump_modify     dump_fix first yes

run             0