From: blaisb Date: Tue, 12 May 2020 02:55:50 +0000 (-0400) Subject: - Changed the default values for the parameters for the 2D case. The default case... X-Git-Tag: v9.2.0-rc2~3^2~4 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=38c8765bfa518f9ffaba1074af627e38020c4652;p=dealii.git - Changed the default values for the parameters for the 2D case. The default case should run easily and produce better results - Finalized resulted for the 2D case - Minor modifications to introduction --- diff --git a/examples/step-70/doc/intro.dox b/examples/step-70/doc/intro.dox index 588219a43a..31e51e68e7 100644 --- a/examples/step-70/doc/intro.dox +++ b/examples/step-70/doc/intro.dox @@ -13,12 +13,11 @@

Massively parallel non-matching grid simulations of fluid structure interaction problems

In this tutorial we consider a mixing problem in the laminar flow regime. -They occur in a wide range of applications ranging from chemical engineering to power +Such problems occur in a wide range of applications ranging from chemical engineering to power generation (e.g. turbomachinery). Mixing problems are particularly hard to solve numerically, because they often involve a container (with fixed boundaries, and possibly complex geometries such as baffles), represented by the domain $\Omega$, and one (or more) immersed and rotating impellers (represented by the domain $\Omega^{\text{imp}}$). - The domain in which we would like to solve the flow equations is the (time depedendent) difference between the two domains, namely: $\Omega\setminus\Omega^{\text{imp}}$. diff --git a/examples/step-70/doc/results.dox b/examples/step-70/doc/results.dox index a4d4b41c2d..43a12c9c76 100644 --- a/examples/step-70/doc/results.dox +++ b/examples/step-70/doc/results.dox @@ -51,10 +51,10 @@ subsection Stokes Immersed Problem set Homogeneous Dirichlet boundary ids = 0 # Initial mesh refinement used for the fluid domain Omega - set Initial fluid refinement = 3 + set Initial fluid refinement = 5 # Initial mesh refinement used for the solid domain Gamma - set Initial solid refinement = 3 + set Initial solid refinement = 5 set Nitsche penalty term = 10 set Number of time steps = 11 set Output frequency = 1 @@ -90,7 +90,7 @@ subsection Stokes Immersed Problem # If the function you are describing represents a vector-valued function # with multiple components, then separate the expressions for individual # components by a semicolon. - set Function expression = t < .500001 ? 5 : -5 # default: 0 + set Function expression = t < .500001 ? 6.283185 : -6.283185 # default: 0 # The names of the variables as they will be used in the function, # separated by commas. By default, the names of variables at which the @@ -116,10 +116,11 @@ subsection Stokes Immersed Problem end subsection Refinement and remeshing - set Maximum number of cells = 1000 + set Maximum number of cells = 20000 set Refinement coarsening fraction = 0.3 set Refinement fraction = 0.3 - set Refinement maximal level = 5 + set Refinement maximal level = 8 + set Refinement minimal level = 5 set Refinement step frequency = 5 set Refinement strategy = fixed_fraction end @@ -177,7 +178,7 @@ subsection Stokes Immersed Problem set Fluid bounding boxes extraction level = 1 set Homogeneous Dirichlet boundary ids = 0 set Initial fluid refinement = 5 - set Initial solid refinement = 3 + set Initial solid refinement = 5 set Nitsche penalty term = 100 set Number of time steps = 501 set Output frequency = 1 @@ -186,7 +187,7 @@ subsection Stokes Immersed Problem set Viscosity = 1 subsection Angular velocity set Function constants = - set Function expression = t < .500001 ? 5 : -5 + set Function expression = t < .500001 ? 6.283185 : -6.283185 # default: 0 set Variable names = x,y,t end subsection Grid generation @@ -198,10 +199,11 @@ subsection Stokes Immersed Problem set Solid grid generator arguments = -.5, -.1: .5, .1: false end subsection Refinement and remeshing - set Maximum number of cells = 1000 + set Maximum number of cells = 20000 set Refinement coarsening fraction = 0.3 set Refinement fraction = 0.3 - set Refinement maximal level = 7 + set Refinement maximal level = 8 + set Refinement minimal level = 5 set Refinement step frequency = 5 set Refinement strategy = fixed_fraction end @@ -238,69 +240,117 @@ parameters to their default value. The default problem generates a co-dimension zero impeller, consisting of a rotating rectangular grid, where the rotation is for half a second in one direction, and half a second in the opposite direction, with constant angular -velocity equal to five. +velocity equal to $\approx 2\Pi rad/s$. Consequently, the impeller does half a rotation +and returns to it's original position. The following animation displays +the velocity magnitude, the motion of the solid impeller and of the +tracer particles.

-

-The output of the program will look like the following: +On one core, the output of the program will look like the following: @code -bash$ mpirun -np 8 ./step-70 test.prm +bash$ mpirun -np 1 ./step-70 test.prm Running StokesImmersedProblem<2> using Trilinos. Cycle 0: Time : 0, time step: 0.002 Number of degrees of freedom: 9539 (8450+1089 -- 0+0) -Tracer particles: 753 -Solid particles: 576 - Solved in 142 iterations. - Number of degrees of freedom: 3790 (3354+436 -- 576+753) +Tracer particles: 337 +Solid particles: 9216 + Solved in 158 iterations. + Number of degrees of freedom: 9845 (8722+1123 -- 9216+337) Cycle 1: Time : 0.002, time step: 0.002 - Solved in 133 iterations. + Solved in 142 iterations. Cycle 2: Time : 0.004, time step: 0.002 - Solved in 148 iterations. + Solved in 121 iterations. Cycle 3: - +Time : 0.006, time step: 0.002 + Solved in 121 iterations. ... - Cycle 499: Time : 0.998, time step: 0.002 - Solved in 167 iterations. + Solved in 199 iterations. Cycle 500: Time : 1, time step: 0.002 - Solved in 156 iterations. - + Solved in 196 iterations. +---------------------------------------------+------------+------------+ -| Total wallclock time elapsed since start | 46.9s | | +| Total wallclock time elapsed since start | 302s | | | | | | | Section | no. calls | wall time | % of total | +---------------------------------+-----------+------------+------------+ -| Assemble Nitsche terms | 501 | 0.73s | 1.6% | -| Assemble Stokes terms | 501 | 1.34s | 2.8% | -| Initial setup | 1 | 0.000827s | 0% | -| Output fluid | 502 | 2.92s | 6.2% | -| Output solid particles | 502 | 1.58s | 3.4% | -| Output tracer particles | 502 | 2.04s | 4.4% | -| Refine | 100 | 1.2s | 2.6% | -| Set solid particle position | 500 | 0.213s | 0.45% | -| Set tracer particle motion | 501 | 1.13s | 2.4% | -| Setup dofs | 101 | 0.82s | 1.7% | -| Solve | 501 | 35.4s | 76% | +| Assemble Nitsche terms | 501 | 43.3s | 14% | +| Assemble Stokes terms | 501 | 21.5s | 7.1% | +| Initial setup | 1 | 0.000792s | 0% | +| Output fluid | 502 | 31.8s | 11% | +| Output solid particles | 502 | 32.2s | 11% | +| Output tracer particles | 502 | 0.61s | 0.2% | +| Refine | 100 | 4.68s | 1.5% | +| Set solid particle position | 500 | 3.34s | 1.1% | +| Set tracer particle motion | 501 | 0.729s | 0.24% | +| Setup dofs | 101 | 2.2s | 0.73% | +| Solve | 501 | 164s | 54% | +---------------------------------+-----------+------------+------------+ @endcode -You may notice that assembling the coupling system is roughly as expensive as -assemblying the Stokes part, and roughly as expensive as tracking the motion -of the particles. +You may notice that assembling the coupling system is more expensive than +assembling the Stokes part. This depends highly on the number of gauss points +(solid particles) that are used to apply the Nitsche restriction. +In the present case, a relatively low number of tracer particles are used. +Consequently, tracking their motion is relatively cheap. + +The following images present the initial and the final configuration of the +simulation domain: + + +

+

+ +
+

+ + +

+

+ +
+

+ +We see that, generally, the tracer particles have somewhat returned to their +original position, although they have been distorted by the flow field. +The following image compares the initial and the final position of the particles +after 1s of flow. + +

+

+ +
+

+ +In this case, we see that the tracer particles that were outside of the swept volume of the +impeller have returned very close to their initial position, whereas those in the swept +volume were slightly more deformed. This deformation is non-physical. It is caused by +the numerical error induced by the explicit Euler scheme used to advect the particles, +by the loss of accuracy due to the fictious domain and, finally, by the discretization +error on the Stokes equations. The first two errors are the leading cause of this deformation +and they could be alleviated by the use of a finer mesh and a lower time step. + +

Three dimensional test case

To play around a little bit, we complicate the fictitious domain (taken from https://grabcad.com/library/lungstors-blower-1), and run a co-dimension one diff --git a/examples/step-70/parameters.prm b/examples/step-70/parameters.prm index 806468b87e..3234de62c4 100644 --- a/examples/step-70/parameters.prm +++ b/examples/step-70/parameters.prm @@ -1,26 +1,38 @@ subsection Stokes Immersed Problem set Final time = 1 - set Homogeneous Dirichlet boundary ids = 0, 1, 2, 3 - set Initial fluid refinement = 4 - set Initial solid refinement = 4 + set Homogeneous Dirichlet boundary ids = 0 + set Initial fluid refinement = 5 + set Initial solid refinement = 5 set Particle insertion refinement = 4 - set Nitsche penalty term = 200 + set Nitsche penalty term = 100 set Number of time steps = 501 set Velocity degree = 2 set Viscosity = 1 subsection Angular velocity set Function constants = - set Function expression = t < .500001 ? 5 : -5 + set Function expression = t < .500001 ? 6.283185 : -6.283185 # default: 0 set Variable names = x,y,t end subsection Grid generation - set Grid one generator = hyper_cube - set Grid one generator arguments = -1: 1: false - set Grid two generator = hyper_rectangle - set Grid two generator arguments = -.5, -.1: .5, .1: false + set Fluid grid generator = hyper_cube + set Fluid grid generator arguments = -1: 1: false set Particle grid generator = hyper_ball set Particle grid generator arguments = 0.3, 0.3: 0.1: false + set Solid grid generator = hyper_rectangle + set Solid grid generator arguments = -.5, -.1: .5, .1: false end + + subsection Refinement and remeshing + set Maximum number of cells = 20000 + set Refinement coarsening fraction = 0.3 + set Refinement fraction = 0.3 + set Refinement maximal level = 8 + set Refinement minimal level = 5 + set Refinement step frequency = 5 + set Refinement strategy = fixed_fraction + end + + subsection Right hand side set Function constants = set Function expression = 0; 0; 0 diff --git a/examples/step-70/step-70.cc b/examples/step-70/step-70.cc index ff328880b3..6f4f76e5f1 100644 --- a/examples/step-70/step-70.cc +++ b/examples/step-70/step-70.cc @@ -60,10 +60,10 @@ namespace LA #include #include +#include #include #include #include -#include #include #include @@ -205,7 +205,7 @@ namespace Step70 // elasticity model in this tutorial, and transform it into a fully fledged // FSI solver. unsigned int initial_fluid_refinement = 5; - unsigned int initial_solid_refinement = 3; + unsigned int initial_solid_refinement = 5; unsigned int particle_insertion_refinement = 3; // To provide a rough description of the fluid domain, we use the method @@ -281,7 +281,9 @@ namespace Step70 // Similarly, we allow for different local refinement strategies. In // particular, we limit the maximum number of refinement levels, in order // to control the minimum size of the fluid grid, and guarantee that it is - // compatible with the solid grid. Additionnaly, we perform local refinement + // compatible with the solid grid. The minimum number of refinement levels + // is also controlled to ensured sufficient accuracy in the + // bulk of the flow. Additionnaly, we perform local refinement // based on standard error estimators on the fluid velocity field. // // We permit the user to choose between the @@ -292,11 +294,12 @@ namespace Step70 // // Refinement may be done every few time steps, instead of continuously, and // we control this value by the `refinement_frequency` parameter: - int max_level_refinement = 7; + int max_level_refinement = 8; + int min_level_refinement = 5; std::string refinement_strategy = "fixed_fraction"; double coarsening_fraction = 0.3; double refinement_fraction = 0.3; - unsigned int max_cells = 1000; + unsigned int max_cells = 20000; int refinement_frequency = 5; // These two functions are used to control the source term of Stokes flow @@ -1439,8 +1442,14 @@ namespace Step70 } for (const auto &cell : fluid_tria.active_cell_iterators()) - if (cell->refine_flag_set() && cell->level() == par.max_level_refinement) - cell->clear_refine_flag(); + { + if (cell->refine_flag_set() && + cell->level() == par.max_level_refinement) + cell->clear_refine_flag(); + if (cell->coarsen_flag_set() && + cell->level() == par.min_level_refinement) + cell->clear_coarsen_flag(); + } parallel::distributed::SolutionTransfer transfer(fluid_dh); @@ -1743,6 +1752,7 @@ namespace Step70 this->prm.enter_subsection("Refinement and remeshing"); this->prm.add_parameter("Refinement step frequency", refinement_frequency); this->prm.add_parameter("Refinement maximal level", max_level_refinement); + this->prm.add_parameter("Refinement minimal level", min_level_refinement); this->prm.add_parameter("Refinement strategy", refinement_strategy, "", @@ -1761,8 +1771,10 @@ namespace Step70 spacedim + 1); }); // and define a meaningful default angular velocity instaed of zero - angular_velocity.declare_parameters_call_back.connect( - [&]() { this->prm.set("Function expression", "t < .500001 ? 5 : -5"); }); + angular_velocity.declare_parameters_call_back.connect([&]() { + this->prm.set("Function expression", + "t < .500001 ? 6.283185 : -6.283185"); + }); } } // namespace Step70