Add consistency test for cv = du/dT at constant V

test/data/consistency-cases.yaml

@@ -32,6 +32,7 @@ ideal-molal-solution:
         "Implementations of g and s are inconsistent. See GitHub Issue #1300"
       gk_eq_hk_minus_T_times_sk:
         "Implementations of g and s are inconsistent. See GitHub Issue #1300"
+      cv_eq_dudT: cv not implemented
   states:
   - {T: 300, P: 101325, molalities: {CH4(aq): 0.01, H2S(aq): 0.03, CO2(aq): 0.1}}
   - {T: 300, P: 2 atm, molalities: {CH4(aq): 0.1, H2S(aq): 0.01, CO2(aq): 0.1}}
@@ -109,6 +110,8 @@ nitrogen-purefluid:
     file: liquidvapor.yaml
     phase: nitrogen
     rtol_fd: 1e-5
+    known-failures:
+      cv_eq_dudT/3: cv not defined in two-phase region
   states:
   - {T: 300, P: 1 atm}
   - {T: 70, P: 1 atm}
@@ -121,6 +124,7 @@ plasma:
     phase: discretized-electron-energy-plasma
     known-failures:
       cp_eq_dhdT/1: Test does not account for distinct electron temperature
+      cv_eq_dudT/1: Test does not account for distinct electron temperature
   states:
   - {T: 300, P: 1 atm, X: {O2: 1.0, O2-: 1e-5, E: 1e-5}}
   - {T: 300, P: 1 atm, X: {E: 1.0}}

test/thermo/consistency.cpp

@@ -163,6 +163,24 @@ TEST_P(TestConsistency, cp_eq_dhdT)
     EXPECT_NEAR(cp_fd, cp_mid, max({rtol_fd * cp_mid, rtol_fd * cp_fd, atol}));
 }
 
+TEST_P(TestConsistency, cv_eq_dudT)
+{
+    double u1 = phase->intEnergy_mole();
+    double cv1 = phase->cv_mole();
+    double T1 = phase->temperature();
+    double dT = 1e-5 * phase->temperature();
+    if (phase->isCompressible()) {
+        phase->setState_TR(T1 + dT, phase->density());
+    } else {
+        phase->setTemperature(T1 + dT);
+    }
+    double u2 = phase->intEnergy_mole();
+    double cv2 = phase->cv_mole();
+    double cv_mid = 0.5 * (cv1 + cv2);
+    double cv_fd = (u2 - u1)/dT;
+    EXPECT_NEAR(cv_fd, cv_mid, max({rtol_fd * cv_mid, rtol_fd * cv_fd, atol}));
+}
+
 INSTANTIATE_TEST_SUITE_P(IdealGas, TestConsistency,
     testing::Combine(
         testing::Values(getSetup("ideal-gas-h2o2")),