DRAFT: Swjones/rk34 integrator unit test

CHANGELOG.md

@@ -3,6 +3,8 @@
 ## Current develop
 
 ### Added (new features/APIs/variables/...)
+- [[PR 1353]](https://github.com/parthenon-hpc-lab/parthenon/pull/1353) RK34 low storage 3rd order 4 stage SSP integrator with CFL <= 2 from Spiteri unit test added
+  & Ruuth 2002, SIAM Journal on Numerical Analysis, 40(2):469–491
 - [[PR 1337]](https://github.com/parthenon-hpc-lab/parthenon/pull/1337) Add task list based timing capabilities
 - [[PR 1331]](https://github.com/parthenon-hpc-lab/parthenon/pull/1331) Add control over whether to include/exclude an output on final signal
 - [[PR 1330]](https://github.com/parthenon-hpc-lab/parthenon/pull/1330) Add userspace mechanisms to control number of comm buffers allocated

tst/unit/test_unit_integrators.cpp

@@ -189,6 +189,18 @@ TEST_CASE("Low storage integrator", "[StagedIntegrator]") {
         REQUIRE(std::abs(u[1] - ufinal[1]) <= 1e-2);
       }
     }
+    WHEN("We integrate with LowStorage rk34") {
+      // still accurate with large timestep
+      constexpr Real dt = 1e-2;
+      auto integrator = MakeIntegrator<LowStorageIntegrator>("rk34");
+      State_t u;
+      GetInitialData(u);
+      Integrate(integrator, Step2SStar, tf, dt, u);
+      THEN("The final state doesn't differ too much from the true solution") {
+        REQUIRE(std::abs(u[0] - ufinal[0]) <= 1e-2);
+        REQUIRE(std::abs(u[1] - ufinal[1]) <= 1e-2);
+      }
+    }
     WHEN("We integrate with LowStorage rk4") {
       // still accurate with large timestep
       constexpr Real dt = 1e-2;