<?xml version="1.0" encoding="UTF-8"?> <simulation xmds-version="2"> <name>le</name> <author>Chaojie Mo</author> <description> The program solves the nonlinear lubrication equation. </description> <features> <benchmark /> <bing /> <fftw plan="patient" /> <auto_vectorise /> <globals> <![CDATA[ const double rho = 6; const double mu = 5; const double lambda = 7.2; const double R = 6.0; const double pi = 3.1415926; ]]> </globals> </features> <geometry> <propagation_dimension> t </propagation_dimension> <transverse_dimensions> <dimension name="z" lattice="120" domain="(-30, 30)" transform="dft"/> </transverse_dimensions> </geometry> <vector name="hv" type="complex" dimensions="z"> <components>h v</components> <initialisation> <![CDATA[ h = R-0.01*R*cos(pi*z/60.0); v = 0; ]]> </initialisation> </vector> <sequence> <integrate algorithm="ARK89" interval="240.0" tolerance="1e-7"> <samples>100</samples> <operators> <integration_vectors>hv</integration_vectors> <operator kind="ex"> <operator_names>Lz</operator_names> <![CDATA[ Lz = i*kz; ]]> </operator> <operator kind="ex"> <operator_names>Lzzz</operator_names> <![CDATA[ Lzzz = -i*kz*kz*kz; ]]> </operator> <operator kind="ex"> <operator_names>Lzz</operator_names> <![CDATA[ Lzz = -kz*kz; ]]> </operator> <![CDATA[ dh_dt = -v*Lz[h] - h*Lz[v]/2.0; dv_dt = -v*Lz[v] + 3.0*mu/rho/h/h*(2.0*h*Lz[h]*Lz[v]+h*h*Lzz[v]) - lambda/rho*((-Lz[h]*sqrt(1+Lz[h]*Lz[h]) - h*Lz[h]*Lzz[h]/sqrt(1+Lz[h]*Lz[h]))/(h*h*(1+Lz[h]*Lz[h])) - (Lzzz[h]*pow(1+Lz[h]*Lz[h],3.0/2.0)-3.0*Lz[h]*Lzz[h]*Lzz[h]*sqrt(1+Lz[h]*Lz[h]))/pow(1+Lz[h]*Lz[h],3.0)); ]]> </operators> </integrate> </sequence> <output> <sampling_group basis="z" initial_sample="yes"> <moments>hR hI vR vI</moments> <dependencies>hv</dependencies> <![CDATA[ hR = h.Re(); hI = h.Im(); vR = v.Re(); vI = v.Im(); ]]> </sampling_group> </output> </simulation>