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[Fluid] Adding low Mach example
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‎fluid_dynamics/validation/README.md

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- [Body-fitted 100 Re cylinder](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_dynamics/validation/body_fitted_cylinder_100Re/README.md)
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- [Embedded moving cylinder](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/embedded_moving_cylinder/README.md)
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- [Low Mach thermally driven cavity](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/low_mach_thermally_driven_cavity/README.md)
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- [Transonic flow around a NACA0012 profile](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/compressible_naca_0012_Ma_0.8/README.md)
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- [Multistage transonic flow around a NACA0012 profile](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/multistage_compressible_naca_0012_Ma_0.8/README.md)
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- [Transonic flow around a NACA0012 profile at a 3° angle](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/compressible_naca_0012_Ma_0.8_aoa_3/README.md)

‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/README.md

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# Low Mach thermally driven cavity
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**Author:** [Rubén Zorrilla](https://github.com/rubenzorrilla)
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**Kratos version:** 10.0
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**Source files:** [Low Mach thermally driven cavity](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_dynamics/validation/low_mach_thermally_driven_cavity/source)
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## Case Specification
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This example solves the well-known thermally driven cavity flow using a low Mach approximation compressible Navier-Stokes solver.
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The problem geometry consists in a 1 x 1 m cavity. No-slip boundary conditions are imposed in all the cavity walls. The initial temperature is 600 ºK. The left wall temperature is set to 960 ºK while the right one is set to 240 ºK. Adiabatic conditions are weakly enforced in top and bottom walls. Pressure is fixed to zero in the top right corner. The fluid is initially at rest so the fluid flow is induced by the thermal effect only. The initial thermodinamic pressure is 101325.0 _Pa_. Gravity (body force) is set to 2.40690342 _m/s<sup>2</sup>_ Note that the material and boundary conditions are set such that the Prandtl number is 0.71 and the Rayleight number is 10<sup>6</sup>.
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Concerning the material, a Newtonian fluid with the characteristic parameters listed below is used.
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* Dynamic viscosity (&mu;): 1e-03 _Kg/m·s_
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* Thermal conductivity (&kappa;): 1.41479 _Kg·m/s<sup>3</sup>·K_
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* Specific heat (c<sub>p<{/sub}>): 1.0045e3 _J/Kg·K_
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* Heat capacity ratio (&gamma;): 1.4
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The time step is 0.25 seconds, while the total simulation time is 30.0 seconds, which is enough to reach an (almost) steady state solution.
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## Results
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The problem is solved using an ASGS stabilised monolithic formulation. A 50x50 divisions structured mesh made up with linear quadrilateral elements is used.
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<p align="center">
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<img src="data/low_mach_thermally_driven_cavity_p.gif" alt="Low Mach thermally driven cavity pressure field [Pa]." style="width: 600px;"/>
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</p>
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<p align="center">
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<img src="data/low_mach_thermally_driven_cavity_v.gif" alt="Low Mach thermally driven cavity velocity field [m/s]." style="width: 600px;"/>
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</p>
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<p align="center">
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<img src="data/low_mach_thermally_driven_cavity_t.gif" alt="Low Mach thermally driven cavity temperature field [K]." style="width: 600px;"/>
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</p>
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<p align="center">
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<img src="data/low_mach_thermally_driven_cavity_rho.gif" alt="Low Mach thermally driven cavity density field [Kg/m<sup>3</sup>]." style="width: 600px;"/>
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</p>
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‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/data/low_mach_thermally_driven_cavity_p.gif

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‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/data/low_mach_thermally_driven_cavity_rho.gif

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‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/data/low_mach_thermally_driven_cavity_t.gif

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‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/data/low_mach_thermally_driven_cavity_v.gif

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‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/source/FluidMaterials.json

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{
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"properties" : [{
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"model_part_name" : "FluidModelPart",
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"properties_id" : 0,
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"Material" : null
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},{
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"model_part_name" : "FluidModelPart.FluidParts_Fluid",
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"properties_id" : 1,
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"Material" : {
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"constitutive_law" : {
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"name" : "Newtonian2DLaw"
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},
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"Variables" : {
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"CONDUCTIVITY" : 1.41479,
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"SPECIFIC_HEAT" : 1.0045e3,
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"DYNAMIC_VISCOSITY" : 1.0e-3,
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"HEAT_CAPACITY_RATIO" : 1.4
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},
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"Tables" : null
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}
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}]
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}

‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/source/MainKratos.py

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import sys
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import time
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import importlib
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import KratosMultiphysics
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import KratosMultiphysics.FluidDynamicsApplication as KratosCFD
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def CreateAnalysisStageWithFlushInstance(cls, global_model, parameters):
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class AnalysisStageWithFlush(cls):
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def __init__(self, model,project_parameters, flush_frequency=10.0):
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super().__init__(model,project_parameters)
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self.flush_frequency = flush_frequency
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self.last_flush = time.time()
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sys.stdout.flush()
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def Initialize(self):
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super().Initialize()
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sys.stdout.flush()
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def ModifyAfterSolverInitialize(self):
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super().ModifyAfterSolverInitialize()
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# Initialize temperature field
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t_0 = 600.0
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for node in self.model.GetModelPart("FluidModelPart.FluidParts_Fluid").Nodes:
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 0, t_0)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 1, t_0)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 2, t_0)
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t_left = 960
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for node in self.model.GetModelPart("FluidModelPart.NoSlip2D_Left").Nodes:
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 0, t_left)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 1, t_left)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 2, t_left)
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t_right = 240
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for node in self.model.GetModelPart("FluidModelPart.NoSlip2D_Right").Nodes:
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 0, t_right)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 1, t_right)
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node.SetSolutionStepValue(KratosMultiphysics.TEMPERATURE, 2, t_right)
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def FinalizeSolutionStep(self):
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super().FinalizeSolutionStep()
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if self.parallel_type == "OpenMP":
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now = time.time()
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if now - self.last_flush > self.flush_frequency:
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sys.stdout.flush()
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self.last_flush = now
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return AnalysisStageWithFlush(global_model, parameters)
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if __name__ == "__main__":
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with open("ProjectParameters.json", 'r') as parameter_file:
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parameters = KratosMultiphysics.Parameters(parameter_file.read())
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analysis_stage_module_name = parameters["analysis_stage"].GetString()
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analysis_stage_class_name = analysis_stage_module_name.split('.')[-1]
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analysis_stage_class_name = ''.join(x.title() for x in analysis_stage_class_name.split('_'))
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analysis_stage_module = importlib.import_module(analysis_stage_module_name)
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analysis_stage_class = getattr(analysis_stage_module, analysis_stage_class_name)
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global_model = KratosMultiphysics.Model()
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simulation = CreateAnalysisStageWithFlushInstance(analysis_stage_class, global_model, parameters)
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simulation.Run()

‎fluid_dynamics/validation/low_mach_thermally_driven_cavity/source/ProjectParameters.json

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{
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"analysis_stage" : "KratosMultiphysics.FluidDynamicsApplication.fluid_dynamics_analysis",
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"problem_data" : {
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"problem_name" : "low_mach_cavity",
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"parallel_type" : "OpenMP",
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"echo_level" : 0,
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"start_time" : 0.0,
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"end_time" : 30.0
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},
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"output_processes" : {
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"gid_output" : [{
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"python_module" : "gid_output_process",
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"kratos_module" : "KratosMultiphysics",
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"process_name" : "GiDOutputProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.fluid_computational_model_part",
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"postprocess_parameters" : {
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"result_file_configuration" : {
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"gidpost_flags" : {
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"GiDPostMode" : "GiD_PostBinary",
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"WriteDeformedMeshFlag" : "WriteDeformed",
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"WriteConditionsFlag" : "WriteConditions",
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"MultiFileFlag" : "SingleFile"
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},
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"file_label" : "time",
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"output_control_type" : "time",
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"output_interval" : 0.5,
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"body_output" : true,
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"node_output" : false,
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"skin_output" : false,
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"plane_output" : [],
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"nodal_results" : ["VELOCITY","PRESSURE","TEMPERATURE","DENSITY"],
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"nodal_nonhistorical_results" : ["NODAL_AREA"],
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"gauss_point_results" : []
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},
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"point_data_configuration" : []
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},
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"output_name" : "gid_output/low_mach_cavity"
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}
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}]
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},
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"solver_settings" : {
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"model_part_name" : "FluidModelPart",
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"domain_size" : 2,
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"solver_type" : "low_mach",
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"material_import_settings" : {
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"materials_filename" : "FluidMaterials.json"
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},
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"echo_level" : 1,
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"compute_reactions" : false,
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"maximum_iterations" : 10,
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"relative_velocity_tolerance" : 0.001,
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"absolute_velocity_tolerance" : 1e-5,
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"relative_pressure_tolerance" : 0.001,
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"absolute_pressure_tolerance" : 1e-5,
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"relative_temperature_tolerance" : 0.001,
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"absolute_temperature_tolerance" : 1e-5,
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"volume_model_part_name" : "FluidParts_Fluid",
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"skin_parts" : ["NoSlip2D_Left","NoSlip2D_Right","NoSlip2D_Top","NoSlip2D_Bottom"],
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"no_skin_parts" : [],
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"time_scheme" : "bdf2",
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"time_stepping" : {
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"automatic_time_step" : false,
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"time_step" : 0.25
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},
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"formulation" : {
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"element_type" : "qsvms"
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},
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"reform_dofs_at_each_step" : false,
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"model_import_settings" : {
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"input_type" : "use_input_model_part"
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},
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"thermodynamic_pressure_settings" : {
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"flow_type" : "closed",
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"value": 101325.0
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}
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},
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"processes" : {
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"initial_conditions_process_list" : [],
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"boundary_conditions_process_list" : [{
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"python_module" : "apply_noslip_process",
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"kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
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"process_name" : "ApplyNoSlipProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Left"
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}
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},{
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"python_module" : "apply_noslip_process",
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"kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
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"process_name" : "ApplyNoSlipProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Right"
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}
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},{
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"python_module" : "apply_noslip_process",
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"kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
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"process_name" : "ApplyNoSlipProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Top"
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}
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},{
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"python_module" : "apply_noslip_process",
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"kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
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"process_name" : "ApplyNoSlipProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Bottom"
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}
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},{
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"python_module" : "assign_scalar_variable_process",
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"kratos_module" : "KratosMultiphysics",
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"process_name" : "AssignScalarVariableProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Left",
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"variable_name" : "TEMPERATURE",
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"interval" : [0.0,"End"],
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"constrained" : true,
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"value" : 960.0
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}
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},{
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"python_module" : "assign_scalar_variable_process",
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"kratos_module" : "KratosMultiphysics",
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"process_name" : "AssignScalarVariableProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.NoSlip2D_Right",
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"variable_name" : "TEMPERATURE",
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"interval" : [0.0,"End"],
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"constrained" : true,
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"value" : 240.0
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}
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},{
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"python_module" : "assign_scalar_variable_process",
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"kratos_module" : "KratosMultiphysics",
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"process_name" : "AssignScalarVariableProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.PressureConstraints2D_TopRightCorner",
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"variable_name" : "PRESSURE",
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"interval" : [0.0,"End"],
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"constrained" : true,
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"value" : 0.0
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}
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}],
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"gravity" : [{
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"python_module" : "assign_vector_by_direction_process",
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"kratos_module" : "KratosMultiphysics",
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"process_name" : "AssignVectorByDirectionProcess",
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"Parameters" : {
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"model_part_name" : "FluidModelPart.FluidParts_Fluid",
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"variable_name" : "BODY_FORCE",
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"modulus" : 2.40690342,
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"constrained" : false,
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"direction" : [0.0,-1.0,0.0]
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}
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}],
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"auxiliar_process_list" : []
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},
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"modelers" : [{
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"name" : "Modelers.KratosMultiphysics.ImportMDPAModeler",
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"parameters" : {
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"input_filename" : "low_mach_cavity",
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"model_part_name" : "FluidModelPart"
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}
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}]
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}

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