Add new R13 P2P1P2P1P1 testcase with validation tests

tests/r13/inputs/r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab.yml

+# General
+# =======
+# - output_folder: Used as output folder
+output_folder: r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab
+
+# Meshes
+# ======
+# - meshes: List of input meshes in h5 format to run simulations on
+meshes:
+  - ../mesh/ring0.h5
+  - ../mesh/ring1.h5
+  - ../mesh/ring2.h5
+  - ../mesh/ring3.h5
+  - ../mesh/ring4.h5
+  # - ../mesh/ring5.h5
+  # - ../mesh/ring6.h5
+  # - ../mesh/ring7.h5
+  # - ../mesh/ring8.h5
+
+# Numerical Parameters
+# ====================
+# - elements: Must contain the fields: theta, s, p, u, sigma
+#   - fields: List of FEM parameters (shape, degree)
+#     - shape: Element shape, e.g. Lagrange
+#     - degree: Element degree, e.g. 2
+# - stabilization: Must contain cip
+#   - cip: Collection of Continous Interior Penalty (CIP) parameters
+#     - enable: Enable CIP stabilization
+#     - delta_theta: Stabilization of grad(T)*grad(T_test) over edge
+#     - delta_u: Stabilization of grad(u)*grad(u_test) over edge
+#     - delta_p: Stabilization of grad(p)*grad(p_test) over edge
+elements:
+  theta:
+    shape: Lagrange
+    degree: 1
+  s:
+    shape: Lagrange
+    degree: 2
+  p:
+    shape: Lagrange
+    degree: 1
+  u:
+    shape: Lagrange
+    degree: 1
+  sigma:
+    shape: Lagrange
+    degree: 2
+stabilization:
+  cip:
+    enable: False
+    delta_theta: 1.0
+    delta_u: 1.0
+    delta_p: 0.01
+
+# Formulation Parameters
+# ======================
+# - nsd: Number of spatial dimensions == 2
+# - mode: Formulation mode, one of heat, stress, r13
+# - kn: Knudsen numberkn
+# - chi_tilde: Refaction coefficient in Maxwell accomodation model
+# - heat_source: Heat source function for mode==heat||r13
+# - mass_source: Mass source function for mode==stress||r13
+# - body_force: Body force for mode==stress||r13
+nsd: 2
+mode: r13
+kn: 1.0
+chi_tilde: 1.0
+heat_source: 0
+mass_source: 0
+body_force: [0,0]
+
+# Boundary Conditions
+# ===================
+# - bcs: Dictionary of all boundary IDs from mesh
+#   - bc_id: must contain theta_w, u_t_w, u_n_w, p_w, epsilon_w
+#     - theta_w: Value for temperature at wall
+#     - u_t_w: Value for tangential velocity at wall
+#     - u_n_w: Value for normal velocity at wall
+#     - p_w: Value for pressure at wall
+#     - epsilon_w: Inflow-model parameter <=> Weight of pressure prescription
+bcs:
+  3000:
+    theta_w: 1
+    u_t_w: 0
+    u_n_w: 0
+    p_w: 0
+    epsilon_w: pow(10,-3)
+  3100:
+    theta_w: 2
+    u_t_w: -1.00 * sin(phi)
+    u_n_w: +1.00 * cos(phi)
+    p_w: -0.27 * cos(phi)
+    epsilon_w: pow(10,+3)
+
+# Convergence Study
+# =================
+# - enable: Enable convergence study on given meshes
+# - exact_solution: Path to exact solution in cpp-format to compare errors
+# - plot: Show errors in matplotlib window. PDF output is always per default.
+# - write_systemmatrix: Writes out systemmatrix (LHS) to use for analysis
+# - rescale_pressure: Rescale numerical pressure result to have zero mean
+# - relative_errors: Use relative errors. If exact sol. is zero, use absolute.
+convergence_study:
+  enable: True
+  exact_solution: esols/1_coeffs_nosources_norot_inflow.cpp
+  plot: False
+  write_systemmatrix: False
+  rescale_pressure: False
+  relative_error: True
+
+# Postprocessing
+# ==============
+# - write_pdfs: Write all solution fields as PDF plot
+# - massflow: List of BC IDs to compute massflow J=int_bc dot(u,n) ds
+postprocessing:
+  write_pdfs: False
+  massflow: []
+
+# Parameter Study
+# ==============
+# - enable: Repeat simulation with different p. values (study)
+# - parameter_key: Key as list, e.g. ["elemenets", "p", "degree"]
+# - parameter_values: List of value for parameter, e.g. [0.01,0.1,1,10]
+parameter_study:
+  enable: False
+  parameter_key: []
+  parameter_values: []
\ No newline at end of file

tests/r13/referrors/r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab/errors.csv

+h,theta_L_2,theta_l_inf,sx_L_2,sx_l_inf,sy_L_2,sy_l_inf,p_L_2,p_l_inf,ux_L_2,ux_l_inf,uy_L_2,uy_l_inf,sigmaxx_L_2,sigmaxx_l_inf,sigmaxy_L_2,sigmaxy_l_inf,sigmayy_L_2,sigmayy_l_inf
+0.9886573325052778,0.0143768913243,0.0167763774855,0.154427796117,0.212905569859,0.170021307007,0.189184423016,0.222665842777,0.38785328282,0.946625073133,0.567225546841,0.310747128191,0.414217805868,0.376671752432,0.462493535845,0.833076883105,0.836036693911,0.546864985397,0.607810788706
+0.6340332990709842,0.0207579137652,0.0367173799369,0.169037418712,0.248093709767,0.163463969828,0.130693891918,0.665027312211,0.8072723145,2.01920543274,0.91507796314,0.701235155631,0.781210911785,1.47078769847,1.04351764263,1.49146487718,1.08353617431,2.00889778669,1.3755469062
+0.32904683851469807,0.0130451011078,0.0214463940876,0.11719988638,0.135578567567,0.0945258805968,0.0635837546267,0.478092455792,0.458272915175,1.30107452488,0.646522741078,0.454477192923,0.649877565913,0.875180306235,0.718588084973,1.07272217111,0.790755661626,1.03959737869,0.753488608423
+0.16754966839339377,0.00244245700739,0.00484554351159,0.0224211862256,0.0282299306717,0.0191812627504,0.0141904437469,0.0888811739689,0.0840260609066,0.220940884681,0.113340275219,0.0826896049548,0.151911670261,0.155970621267,0.128324961683,0.195690972003,0.153115738912,0.190054619914,0.139421512179
+0.08734460120995041,0.000595068041661,0.00121440933827,0.0055147176246,0.00700562569891,0.00471691302173,0.00347684971707,0.0217752311678,0.0216173663209,0.0531285069094,0.0331765062864,0.0204957947248,0.0441530177482,0.0379894104042,0.0316570167234,0.0479717016566,0.0387767133382,0.0457767021787,0.0339001090382

tests/r13/test_r13_convergence.py

@@ -161,3 +161,40 @@ class TestR13Convergence(object):
         errors = name + "/" + "errors.csv"
         referrors = "referrors/" + name + "/errors.csv"
         self.compare_errors(errors, referrors)
+
+    def test_r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab(self):
+        r"""
+        Execute full linear R13 system test and check with reference errors.
+        Use Generalized Taylor-Hood elements (P2P1P2P1P1) w.o. stabilization.
+
+        Test case is similar to  [TOR2017]_.
+
+        .. [TOR2017] Torrilhon, M. et al. (2017). “Hierarchical Boltzmann
+            simulations and model error estimation”. In: Journal of
+            Computational Physics 342 (2017), pp. 66–84.
+
+        ==================== ===================================================
+        Parameter     Value
+        ==================== ===================================================
+        :math:`Kn`           :math:`1.0`
+        :math:`\dot{m}`      :math:`0`
+        :math:`r`            :math:`0`
+        :math:`\theta_w^1`   :math:`1.0`
+        :math:`v_t^1`        :math:`0`
+        :math:`v_n^1`        :math:`0`
+        :math:`p_w^1`        :math:`0`
+        :math:`\epsilon_w^1` :math:`10^{-3}`
+        :math:`\theta_w^2`   :math:`2.0`
+        :math:`v_t^2`        :math:`-1.00 \sin(\phi)`
+        :math:`v_n^2`        :math:`+1.00 \cos(\phi)`
+        :math:`p_w^2`        :math:`-0.27 \cos(\phi)`
+        :math:`\epsilon_w^2` :math:`10^{3}`
+        Elements             :math:`P_1P_2P_1P_1P_2`
+        Stabilization        Off
+        ==================== ===================================================
+        """
+        name = "r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab"
+        self.run_solver("inputs/" + name + ".yml")
+        errors = name + "/" + "errors.csv"
+        referrors = "referrors/" + name + "/errors.csv"
+        self.compare_errors(errors, referrors)