C内核按库功能拆解，编译结果缓存区构建，编译过程与已有缓存结果对照功能实现
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/* Helium Peng-Robinson and compressible-orifice kernels.
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* Ported from the project's Python physical equations; validated independently
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* against Python at ordinary, reverse-flow and contact trial states.
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*/
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#include "component_properties_internal.h"
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#include "component_constants_internal.h"
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#include <math.h>
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#include <stddef.h>
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#define RU 8.31446261815324
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#define MOLAR_MASS 0.004002602
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#define TC 5.1953
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#define PC 227460.0
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#define OMEGA (-0.382)
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static const double pr_a=.457235583*RU*RU*TC*TC/PC;
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static const double pr_b=.07779607*RU*TC/PC;
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static const double kappa=.37464+1.54226*OMEGA-.26992*OMEGA*OMEGA;
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static const double rg=RU/MOLAR_MASS;
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NATIVE_COMPONENT_INTERNAL const NativeMedium helium_medium={1,RU/MOLAR_MASS,2.5*RU/MOLAR_MASS,293.15,0,1.96e-5,293.15,79.4};
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NATIVE_COMPONENT_INTERNAL int same_medium(const NativeMedium *a,const NativeMedium *b) {
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return a->real_helium==b->real_helium && a->R==b->R && a->cp==b->cp &&
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a->Tref==b->Tref && a->slope==b->slope && a->mu==b->mu && a->muT==b->muT && a->S==b->S;
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}
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void native_properties_init(NativePropertyCache *cache,NativePropertyState *states,size_t capacity) {
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cache->states=states;cache->count=0;cache->capacity=states?capacity:0;
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}
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static NativePropertyState *property_new(NativePropertyCache *cache,const NativeMedium *m,
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double p,double T,NativePropertyState *scratch) {
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int valid=p>0 && T>0 && isfinite(p) && isfinite(T);
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NativePropertyState *s=valid && cache && cache->count<cache->capacity ? &cache->states[cache->count++] : scratch;
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*s=(NativePropertyState){0};s->medium=*m;s->p=p;s->T=T;s->valid=valid?NATIVE_PROPERTY_PT:0;
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return s;
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}
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NATIVE_COMPONENT_INTERNAL NativePropertyState *property_pt(NativePropertyCache *cache,const NativeMedium *m,
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double p,double T,NativePropertyState *scratch) {
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if(cache)for(size_t i=0;i<cache->count;i++) {
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NativePropertyState *s=&cache->states[i];
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if((s->valid&NATIVE_PROPERTY_PT) && s->p==p && s->T==T && same_medium(&s->medium,m))return s;
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}
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return property_new(cache,m,p,T,scratch);
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}
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NATIVE_COMPONENT_INTERNAL double property_density(NativePropertyState *s) {
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if(!(s->valid&NATIVE_PROPERTY_RHO)) {
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s->rho=native_density(&s->medium,s->p,s->T);
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if(s->rho>0 && isfinite(s->rho))s->valid|=NATIVE_PROPERTY_RHO;
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}
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return s->rho;
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}
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NATIVE_COMPONENT_INTERNAL double property_viscosity(NativePropertyState *s) {
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if(!(s->valid&NATIVE_PROPERTY_MU)) {
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s->mu=native_viscosity(&s->medium,s->T,0);
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if(s->mu>0 && isfinite(s->mu))s->valid|=NATIVE_PROPERTY_MU;
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}
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return s->mu;
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}
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static void remember_gas(NativePropertyCache *cache,const NativeMedium *m,const NativeGas *gas) {
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/* Below helium's critical temperature retain the existing vapor-root/PH
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selection. A future phase-aware medium contract can carry that state. */
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if(!cache || (m->real_helium && gas->T<=TC))return;
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NativePropertyState scratch,*s=property_pt(cache,m,gas->p,gas->T,&scratch);
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if(!(s->valid&NATIVE_PROPERTY_PT) || !isfinite(gas->h))return;
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if((s->valid&NATIVE_PROPERTY_H) && s->h!=gas->h)
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s=property_new(cache,m,gas->p,gas->T,&scratch);
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s->h=gas->h;s->valid|=NATIVE_PROPERTY_H;
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if(gas->rho>0 && isfinite(gas->rho)){s->rho=gas->rho;s->valid|=NATIVE_PROPERTY_RHO;}
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}
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double native_temperature_ph_context(NativePropertyCache *cache,const NativeMedium *m,double p,double h) {
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if(cache)for(size_t i=0;i<cache->count;i++) {
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NativePropertyState *s=&cache->states[i];
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if((s->valid&NATIVE_PROPERTY_H) && s->p==p && s->h==h && same_medium(&s->medium,m))return s->T;
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}
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double T=native_temperature_ph(m,p,h);
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if(cache && isfinite(h) && T>0 && isfinite(T) && p>0 && isfinite(p)) {
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NativePropertyState scratch,*s=property_pt(cache,m,p,T,&scratch);
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if((s->valid&NATIVE_PROPERTY_H) && s->h!=h)s=property_new(cache,m,p,T,&scratch);
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s->h=h;s->valid|=NATIVE_PROPERTY_H;
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}
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return T;
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}
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double native_density_context(NativePropertyCache *cache,const NativeMedium *m,double p,double T) {
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NativePropertyState scratch;return property_density(property_pt(cache,m,p,T,&scratch));
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}
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static double cube_root(double x) { return x==0 ? 0 : copysign(pow(fabs(x),1.0/3.0),x); }
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static void attraction(double T, double *a, double *da, double *dda) {
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double tr=T/TC, sr=sqrt(tr), base=1+kappa*(1-sr);
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*a=pr_a*base*base;
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*da=pr_a*(-base*kappa/(TC*sr));
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*dda=pr_a*kappa/(2*TC*TC)*(kappa/tr+base/(tr*sr));
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}
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static double z_factor(double p,double T) {
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double a,da,dda; attraction(T,&a,&da,&dda);
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double A=a*p/(RU*RU*T*T), B=pr_b*p/(RU*T);
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double ca=-(1-B),cb=A-3*B*B-2*B,cc=-(A*B-B*B-B*B*B);
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double pp=cb-ca*ca/3,qq=2*ca*ca*ca/27-ca*cb/3+cc;
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double disc=pow(qq/2,2)+pow(pp/3,3),off=-ca/3,roots[3]; int n;
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if(disc>1e-14) { roots[0]=cube_root(-qq/2+sqrt(disc))+cube_root(-qq/2-sqrt(disc))+off;n=1; }
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else if(fabs(disc)<=1e-14) { double u=cube_root(-qq/2);roots[0]=2*u+off;roots[1]=-u+off;n=2; }
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else { if(pp>=0) return NAN; double radius=2*sqrt(-pp/3);
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double arg=(3*qq/(2*pp))*sqrt(-3/pp),theta=acos(fmax(-1,fmin(1,arg)))/3;
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for(int i=0;i<3;i++) { roots[i]=radius*cos(theta-2*PI*i/3)+off; }
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n=3;
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}
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double z=-INFINITY;for(int i=0;i<n;i++) if(roots[i]>B && isfinite(roots[i])) z=fmax(z,roots[i]);
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return isfinite(z)?z:NAN;
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}
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static double density(double p,double T) { return MOLAR_MASS/(z_factor(p,T)*RU*T/p); }
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static double log_volume(double rho) {
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double v=MOLAR_MASS/rho,sq=sqrt(2.0);
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return log((v+(1+sq)*pr_b)/(v+(1-sq)*pr_b))/(2*sq*pr_b*MOLAR_MASS);
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}
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static double u_departure(double T,double rho) {
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double a,da,dda;attraction(T,&a,&da,&dda);return (T*da-a)*log_volume(rho);
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}
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static double h_departure(double p,double T) {
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double a,da,dda;attraction(T,&a,&da,&dda);
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double z=z_factor(p,T),B=pr_b*p/(RU*T),sq=sqrt(2.0);
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double dep=RU*T*(z-1)+(T*da-a)*log((z+(1+sq)*B)/(z+(1-sq)*B))/(2*sq*pr_b);
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return dep/MOLAR_MASS;
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}
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static double u_ideal(double T) { return rg*(1.5*T-745.375); }
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static double h_ideal(double T) { return rg*(2.5*T-745.375); }
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static double temperature_u(double u) { return (u/rg+745.375)/1.5; }
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static double temperature_h(double h) { return (h/rg+745.375)/2.5; }
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static double pressure_rho(double T,double rho) {
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double v=MOLAR_MASS/rho,a,da,dda;attraction(T,&a,&da,&dda);
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if(v<=pr_b || T<=0) return NAN;
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return RU*T/(v-pr_b)-a/(v*(v+pr_b)+pr_b*(v-pr_b));
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}
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static NativeGas gas_properties(double m,double U,double V) {
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NativeGas g;g.rho=m/V;g.u=U/m;
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double T=fmax(temperature_u(g.u),2.2);
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for(int i=0;i<16;i++) { double next=fmax(temperature_u(g.u-u_departure(T,g.rho)),2.2);
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int done=fabs(next-T)<=1e-10*fmax(T,1);T=next;if(done) break; }
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g.T=T;g.p=pressure_rho(T,g.rho);
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/* Same energy reference as u_ideal/h_ideal. Avoid a redundant cubic solve
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in the single-root region; preserve vapor-root semantics below TC. */
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g.h=T>TC ? g.u+g.p/g.rho : h_ideal(T)+h_departure(g.p,T);return g;
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}
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static double temperature_ph(double p,double h) {
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double T=fmax(temperature_h(h),2.2);
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for(int i=0;i<16;i++) { double next=fmax(temperature_h(h-h_departure(p,T)),2.2);
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int done=fabs(next-T)<=1e-10*fmax(T,1);T=next;if(done) break; }return T;
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}
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static void local_isentropic(NativePropertyState *s) {
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if(s->valid&NATIVE_PROPERTY_ISENTROPIC)return;
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double p=s->p,T=s->T,rho=property_density(s),v=MOLAR_MASS/rho,a,da,dda;attraction(T,&a,&da,&dda);
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double d=v*(v+pr_b)+pr_b*(v-pr_b);
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double dpT=RU/(v-pr_b)-da/d;
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double dpR=(-RU*T/pow(v-pr_b,2)+a*2*(v+pr_b)/(d*d))*(-MOLAR_MASS/(rho*rho));
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double cv=1.5*rg+T*dda*log_volume(rho);
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double cp=cv+T*dpT*dpT/(rho*rho*dpR),gamma=cp/cv;
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s->isentropic_factor=p/(rho*dpR*gamma);s->isentropic_exponent=p*(gamma-1)/(gamma*T*dpT);
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if(isfinite(s->isentropic_factor) && isfinite(s->isentropic_exponent))s->valid|=NATIVE_PROPERTY_ISENTROPIC;
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}
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static double isentropic(NativePropertyCache *cache,NativePropertyState *up,double pd) {
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local_isentropic(up);if(pd>=up->p)return up->isentropic_factor;
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double Td=fmax(up->T*pow(fmax(pd/up->p,1e-12),up->isentropic_exponent),2.2);
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NativePropertyState scratch,*down=property_pt(cache,&up->medium,fmax(pd,1),Td,&scratch);
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local_isentropic(down);return .5*(up->isentropic_factor+down->isentropic_factor);
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}
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static double subsonic_cm(double r,double gamma,double rho,double T,double p) {
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return sqrt(fmax(2/(1-gamma)*rho*T/p*(pow(r,2*gamma)-pow(r,1+gamma)),0));
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}
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NATIVE_COMPONENT_INTERNAL void state_valve(NativePropertyCache *cache,NativePropertyState *up,double pd,double *cm,double *vel) {
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double p=up->p,T=up->T;pd=fmax(fmin(pd,p),0);
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const NativeMedium *m=&up->medium;
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double cp=m->cp+m->slope*(T-m->Tref);
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double factor=m->real_helium?isentropic(cache,up,pd):(cp-m->R)/cp;
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double g=fmax(1e-9,fmin(1-1e-9,factor)),rho=fmax(property_density(up),1e-12);
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double r=fmax(pd/p,0),critical=pow(2*g/(g+1),1/(1-g)),eff;
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if(r<=critical) { eff=critical;*cm=sqrt(2/(1+g)*rho*T/p)*pow(2*g/(g+1),g/(1-g));*vel=sqrt(2/(1+g)*p/rho); }
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else { eff=r;*cm=subsonic_cm(r,g,rho,T,p);*vel=sqrt(fmax(2/(1-g)*p/rho*(1-pow(r,1-g)),0)); }
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double ref=subsonic_cm(.9999,g,rho,T,p);
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if(*cm>0 && ref>0) { double smooth=tanh(fmax(12*fabs(*cm/ref)*log(eff)/log(.9999),0));*cm*=smooth;*vel*=smooth; }
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}
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NATIVE_COMPONENT_INTERNAL void medium_valve(NativePropertyCache *cache,const NativeMedium *m,double p,double pd,double T,double *cm,double *vel) {
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NativePropertyState scratch,*up=property_pt(cache,m,fmax(p,1),fmax(T,1),&scratch);
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state_valve(cache,up,pd,cm,vel);
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}
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int native_gas_init(double p, double T, double volume, double *mU) {
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if (!(p > 0 && T >= 2.2 && volume > 0)) return 0;
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double rho = density(p, T);
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mU[0] = rho * volume;
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mU[1] = mU[0] * (u_ideal(T) + u_departure(T, rho));
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return isfinite(mU[0]) && isfinite(mU[1]) && mU[0] > 0;
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}
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int native_gas(double m, double U, double volume, NativeGas *gas) {
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if (!(m > 0 && volume > 0) || !isfinite(U)) return 0;
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*gas = gas_properties(m, U, volume);
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return gas->p > 0 && isfinite(gas->p) && isfinite(gas->h);
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}
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int native_gas_context(NativePropertyCache *cache,double m,double U,double V,NativeGas *gas) {
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int ok=native_gas(m,U,V,gas);if(ok)remember_gas(cache,&helium_medium,gas);return ok;
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}
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static double ideal_temperature(const NativeMedium *m, double energy, double c) {
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double delta = energy - c*m->Tref;
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if (fabs(m->slope) <= 1e-15) return m->Tref + delta/c;
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double root = sqrt(fmax(c*c + 2*m->slope*delta, 0));
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double a = (-c+root)/m->slope, b = (-c-root)/m->slope;
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return m->Tref + (fabs(a)<=fabs(b) ? a : b);
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}
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int native_medium_init(const NativeMedium *medium, double p, double T, double V,
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int legacy_ideal_initial, double *mU) {
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if (!(p>0 && T>0 && V>0)) return 0;
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if (medium->real_helium && !legacy_ideal_initial) return native_gas_init(p,T,V,mU);
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double mass=p*V/(medium->R*T),dt=T-medium->Tref;
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double u=medium->real_helium?u_ideal(T):(medium->cp-medium->R)*T+.5*medium->slope*dt*dt;
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mU[0]=mass;mU[1]=mass*u;
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return isfinite(mU[0]) && isfinite(mU[1]);
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}
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double native_density(const NativeMedium *m, double p, double T) {
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return m->real_helium ? density(p,T) : p/(m->R*T);
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}
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double native_temperature_ph(const NativeMedium *m, double p, double h) {
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return m->real_helium ? temperature_ph(p,h) : ideal_temperature(m,h,m->cp);
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}
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double native_viscosity(const NativeMedium *m, double T, int diagnostic) {
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/* Retain the ABI argument; flow and diagnostics use the same property. */
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(void)diagnostic;
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if (m->real_helium)
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return 1e-7*exp(.7501594*log(T)+35.76324/T-2212.129/(T*T)+.9212635);
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return m->mu*pow(T/m->muT,1.5)*(m->muT+m->S)/(T+m->S);
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}
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int native_medium_gas(const NativeMedium *medium, double m, double U, double V, NativeGas *g) {
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if (medium->real_helium) return native_gas(m,U,V,g);
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if (!(m>0 && V>0)) return 0;
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g->u=U/m; g->rho=m/V;
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g->T=ideal_temperature(medium,g->u,medium->cp-medium->R);
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g->p=g->rho*medium->R*g->T;
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double dt=g->T-medium->Tref;
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g->h=medium->cp*g->T+.5*medium->slope*dt*dt;
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return g->T>0 && isfinite(g->p) && isfinite(g->h);
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}
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int native_medium_gas_context(NativePropertyCache *cache,const NativeMedium *m,double mass,double U,double V,NativeGas *g) {
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int ok=native_medium_gas(m,mass,U,V,g);if(ok)remember_gas(cache,m,g);return ok;
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}
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