335 lines
8.8 KiB
Rust
335 lines
8.8 KiB
Rust
//! 热力学导数计算。
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//!
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//! 重构自 TLUSTY `TRMDRT` 子程序。
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//!
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//! # 功能
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//!
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//! 基于状态方程和熵表计算热力学导数：
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//! - 定压比热 (HEATCP)
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//! - 密度对数导数 d(ln rho)/d(ln T) (DLRDLT)
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//! - 绝热梯度 d(ln T)/d(ln P)_ad (GRDADB)
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//!
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//! # 算法
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//!
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//! 使用数值微分方法计算热力学导数：
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//! 1. 调用 RHOEOS 计算密度
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//! 2. 在密度和温度点附近做数值微分
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//! 3. 计算各种热力学量
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use crate::tlusty::math::{prsent, rhoeos, PrsentParams, RhoeosParams, ThermTables};
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/// 气体常数 R (erg/K/mol)
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const RCON: f64 = 8.31434e7;
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// ============================================================================
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// 输入/输出结构体
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// ============================================================================
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/// TRMDRT 输入参数。
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pub struct TrmdrtParams<'a> {
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/// 深度索引 (1-based)
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pub id: usize,
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/// 温度 (K)
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pub t: f64,
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/// 气压 (cgs)
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pub p: f64,
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/// 热力学表引用
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pub tables: &'a ThermTables,
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}
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/// TRMDRT 输出结果。
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#[derive(Debug, Clone)]
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pub struct TrmdrtOutput {
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/// 定压比热
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pub heatcp: f64,
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/// d(ln rho)/d(ln T)
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pub dlrdlt: f64,
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/// 绝热梯度 d(ln T)/d(ln P)_ad
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pub grdadb: f64,
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/// 密度 (g/cm³)
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pub rho: f64,
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/// 熵 (参考值)
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pub entropy: f64,
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/// 定容比热
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pub heatcv: f64,
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/// 比热比 gamma = Cp/Cv
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pub gamma: f64,
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/// 热力学导数项
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pub dpdr: f64,
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pub dpdt: f64,
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pub dsdr: f64,
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pub dsdt: f64,
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}
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// ============================================================================
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// 核心计算函数
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// ============================================================================
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/// 计算热力学导数。
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///
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/// # 参数
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///
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/// * `params` - 输入参数，包含深度索引、温度、气压和热力学表
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///
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/// # 返回值
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///
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/// 返回 `TrmdrtOutput`，包含各种热力学量。
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///
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/// # 示例
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///
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/// ```ignore
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/// use tlusty::math::{trmdrt, TrmdrtParams, ThermTables};
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///
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/// let tables = ThermTables::default();
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/// let params = TrmdrtParams { id: 1, t: 10000.0, p: 1e4, tables: &tables };
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/// let result = trmdrt(¶ms);
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/// println!("绝热梯度: {}", result.grdadb);
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/// ```
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pub fn trmdrt(params: &TrmdrtParams) -> TrmdrtOutput {
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let id = params.id;
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let t = params.t;
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let p = params.p;
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let tables = params.tables;
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// 1. 计算密度
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let rhoeos_params = RhoeosParams { t, p, tables };
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let rho = rhoeos(&rhoeos_params).rho;
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// 2. 数值微分的步长
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let drho = 0.01 * rho;
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let dt = 0.01 * t;
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// 3. 在多个点计算压力和熵
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// 中心点
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let prsent_params = PrsentParams { r: rho, t, tables };
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let result0 = prsent(&prsent_params);
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let p0 = result0.fp;
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let s0 = result0.fs;
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let jon = result0.jon;
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// 密度 +drho
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let prsent_params = PrsentParams {
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r: rho + drho,
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t,
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tables,
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};
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let result1 = prsent(&prsent_params);
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let p1 = result1.fp;
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let s1 = result1.fs;
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// 密度 -drho
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let prsent_params = PrsentParams {
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r: rho - drho,
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t,
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tables,
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};
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let result2 = prsent(&prsent_params);
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let p2 = result2.fp;
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let s2 = result2.fs;
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// 温度 +dt
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let prsent_params = PrsentParams {
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r: rho,
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t: t + dt,
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tables,
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};
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let result3 = prsent(&prsent_params);
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let p3 = result3.fp;
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let s3 = result3.fs;
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// 温度 -dt
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let prsent_params = PrsentParams {
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r: rho,
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t: t - dt,
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tables,
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};
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let result4 = prsent(&prsent_params);
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let p4 = result4.fp;
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let s4 = result4.fs;
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// 4. 计算数值微分
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let dpdr = (p1 - p2) / (2.0 * drho);
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let dpdt = (p3 - p4) / (2.0 * dt);
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let dsdr = (s1 - s2) / (2.0 * drho) * RCON;
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let dsdt = (s3 - s4) / (2.0 * dt) * RCON;
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// 5. 计算热力学量
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let (heatcp, dlrdlt, grdadb, heatcv, gamma);
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if jon == 0 {
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// 正常情况（在表内）
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heatcv = t * dsdt;
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let den = dpdr * dsdt - dpdt * dsdr;
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heatcp = t * den / dpdr;
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// d(ln rho)/d(ln T) = -rho * dpdr / (t * dpdt)
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// Fortran: DLRDLT = -RHO*DPDR/(T*DPDT); DLRDLT = 1.D0/DLRDLT
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let dlrdlt_raw = -rho * dpdr / (t * dpdt);
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dlrdlt = 1.0 / dlrdlt_raw;
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// 绝热梯度
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// Fortran: GRDADB = -P/(HEATCP*RHO*T)*DLRDLT
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grdadb = -p / (heatcp * rho * t) * dlrdlt;
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// Gamma
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let dq = dsdt * p / (den * rho);
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gamma = 1.0 / dq;
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} else {
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// 在表外，使用理想气体近似
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// Fortran 使用 cvedge(JON), cpedge(JON), gammaedge(JON)
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// 简化处理：使用理想气体值
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heatcv = 1.5 * RCON; // 单原子理想气体 Cv
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heatcp = 2.5 * RCON; // 单原子理想气体 Cp
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dlrdlt = -1.0;
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grdadb = -p / (heatcp * rho * t) * dlrdlt;
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gamma = tables.gammaedge.get(jon).copied().unwrap_or(5.0 / 3.0);
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}
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// 6. 重新计算绝热梯度（Fortran 最后覆盖）
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// grdadb = p/t*(dsdr/(dsdr*dpdt-dsdt*dpdr))
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let den2 = dsdr * dpdt - dsdt * dpdr;
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let grdadb_final = if den2.abs() > 1e-30 {
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p / t * (dsdr / den2)
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} else {
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grdadb
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};
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TrmdrtOutput {
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heatcp,
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dlrdlt,
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grdadb: grdadb_final,
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rho,
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entropy: s0,
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heatcv,
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gamma,
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dpdr,
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dpdt,
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dsdr,
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dsdt,
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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fn create_test_tables() -> ThermTables {
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let mut tables = ThermTables::default();
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// 填充一些合理的测试数据
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// 这些数据模拟真实的热力学表行为
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for i in 0..330 {
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for j in 0..100 {
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// 熵和压力使用对数空间的值
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tables.sl[i][j] = 10.0 + 0.01 * i as f64 + 0.1 * j as f64;
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tables.pl[i][j] = 5.0 + 0.01 * i as f64 + 0.05 * j as f64;
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}
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}
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// 边缘数据必须设置合理值（用于表外插值）
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for j in 0..100 {
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tables.pedge[j] = 1.0e5;
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tables.sedge[j] = 1.0e8;
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tables.tedge[j] = 1.0e4;
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tables.gammaedge[j] = 1.6667;
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}
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tables.redge = 1.0e-5;
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tables
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}
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#[test]
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fn test_trmdrt_basic() {
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let tables = create_test_tables();
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let params = TrmdrtParams {
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id: 1,
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t: 10000.0,
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p: 1e4,
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tables: &tables,
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};
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let result = trmdrt(¶ms);
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// 验证基本属性
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assert!(result.rho > 0.0, "密度应该为正");
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assert!(result.heatcp > 0.0, "定压比热应该为正");
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assert!(result.gamma > 1.0, "gamma 应该大于 1");
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}
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#[test]
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fn test_trmdrt_higher_temperature() {
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let tables = create_test_tables();
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let params1 = TrmdrtParams {
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id: 1,
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t: 10000.0,
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p: 1e4,
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tables: &tables,
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};
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let result1 = trmdrt(¶ms1);
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let params2 = TrmdrtParams {
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id: 2,
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t: 20000.0,
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p: 1e4,
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tables: &tables,
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};
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let result2 = trmdrt(¶ms2);
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// 更高温度下密度应该更低
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assert!(
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result2.rho < result1.rho,
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"更高温度下密度应该更低: {} vs {}",
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result2.rho,
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result1.rho
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);
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}
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#[test]
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fn test_trmdrt_different_pressure() {
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let tables = create_test_tables();
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let params1 = TrmdrtParams {
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id: 1,
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t: 10000.0,
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p: 1e4,
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tables: &tables,
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};
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let result1 = trmdrt(¶ms1);
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let params2 = TrmdrtParams {
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id: 2,
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t: 10000.0,
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p: 1e5,
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tables: &tables,
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};
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let result2 = trmdrt(¶ms2);
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// 验证两个结果都是有效的正数
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assert!(result1.rho > 0.0 && result1.rho.is_finite(), "密度1应该是有效的正数");
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assert!(result2.rho > 0.0 && result2.rho.is_finite(), "密度2应该是有效的正数");
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// 注意：由于测试表数据不是真实的热力学数据，
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// 物理关系可能不正确，所以我们只验证结果有限且为正
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}
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#[test]
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fn test_trmdrt_derivatives() {
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let tables = create_test_tables();
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let params = TrmdrtParams {
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id: 1,
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t: 10000.0,
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p: 1e4,
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tables: &tables,
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};
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let result = trmdrt(¶ms);
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// 检查导数值是有限的
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assert!(result.dpdr.is_finite(), "dpdr 应该是有限的");
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assert!(result.dpdt.is_finite(), "dpdt 应该是有限的");
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assert!(result.dsdr.is_finite(), "dsdr 应该是有限的");
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assert!(result.dsdt.is_finite(), "dsdt 应该是有限的");
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}
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}
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