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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | |||
| 8 | #ifndef DUMUX_ONEP_ROTATION_SYMMETRY_PROBLEM_HH | ||
| 9 | #define DUMUX_ONEP_ROTATION_SYMMETRY_PROBLEM_HH | ||
| 10 | |||
| 11 | // ## The problem class (`problem.hh`) | ||
| 12 | // This file contains the __problem class__ which defines the initial and boundary | ||
| 13 | // conditions for the single-phase flow simulation. | ||
| 14 | // [[content]] | ||
| 15 | // ### Includes | ||
| 16 | #include <cmath> // for `std::log` | ||
| 17 | #include <dumux/common/boundarytypes.hh> // for `BoundaryTypes` | ||
| 18 | #include <dumux/common/properties.hh> // for `GetPropType` | ||
| 19 | #include <dumux/common/parameters.hh> // for `getParam` | ||
| 20 | #include <dumux/porousmediumflow/problem.hh> // for `PorousMediumFlowProblem` | ||
| 21 | |||
| 22 | // ### The problem class | ||
| 23 | // We enter the problem class where all necessary boundary conditions and initial conditions are set for our simulation. | ||
| 24 | // As this is a porous medium flow problem, we inherit from the base class `PorousMediumFlowProblem`. | ||
| 25 | namespace Dumux { | ||
| 26 | |||
| 27 | template<class TypeTag> | ||
| 28 | 1 | class RotSymExampleProblem : public PorousMediumFlowProblem<TypeTag> | |
| 29 | { | ||
| 30 | using ParentType = PorousMediumFlowProblem<TypeTag>; | ||
| 31 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 32 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 33 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 34 | using BoundaryTypes = Dumux::BoundaryTypes<PrimaryVariables::size()>; | ||
| 35 | using Element = typename GridGeometry::GridView::template Codim<0>::Entity; | ||
| 36 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 37 | |||
| 38 | public: | ||
| 39 | // In the constructor, we obtain a number of parameters, related to fluid | ||
| 40 | // properties and boundary conditions, from the input file. | ||
| 41 | // [[codeblock]] | ||
| 42 | 1 | RotSymExampleProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 43 |
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3 | : ParentType(gridGeometry) |
| 44 | { | ||
| 45 | // fluid properties | ||
| 46 |
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1 | k_ = getParam<Scalar>("SpatialParams.Permeability"); |
| 47 |
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1 | nu_ = getParam<Scalar>("Component.LiquidKinematicViscosity"); |
| 48 |
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1 | rho_ = getParam<Scalar>("Component.LiquidDensity"); |
| 49 | |||
| 50 | // The inner radius r1 can be determined from the grid | ||
| 51 |
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2 | r1_ = gridGeometry->bBoxMin()[0]; |
| 52 | |||
| 53 | // boundary conditions | ||
| 54 |
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1 | q1_ = getParam<Scalar>("Problem.Q1"); // mass flux into the domain at r1 in kg/s/m |
| 55 |
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1 | p1_ = getParam<Scalar>("Problem.P1"); // pressure at the inner boundary at r1 |
| 56 | 1 | } | |
| 57 | // [[/codeblock]] | ||
| 58 | |||
| 59 | // #### Specify the types of boundary conditions | ||
| 60 | // This function is used to define the type of boundary conditions used depending on the location. | ||
| 61 | // Two types of boundary conditions can be specified: Dirichlet or Neumann boundary condition. | ||
| 62 | // On a Dirichlet boundary, the values of the primary variables need to be fixed. On a Neumann | ||
| 63 | // boundary condition, values for derivatives need to be fixed. Here, we use Dirichlet boundary | ||
| 64 | // conditions on all boundaries. | ||
| 65 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const | |
| 66 | { | ||
| 67 |
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10 | BoundaryTypes values; |
| 68 |
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10 | values.setAllDirichlet(); |
| 69 | ✗ | return values; | |
| 70 | } | ||
| 71 | |||
| 72 | // #### Specify Dirichlet boundary condition values | ||
| 73 | // This function is used to specify the values of the primary variables at Dirichlet boundaries. | ||
| 74 | // Here, we evaluate the analytical solution (see below) to define the pressures at the boundaries. | ||
| 75 | PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const | ||
| 76 | 10 | { return exactSolution(globalPos); } | |
| 77 | |||
| 78 | // #### Analytical solution | ||
| 79 | // The analytical solution to the problem of this example reads: | ||
| 80 | // | ||
| 81 | // ```math | ||
| 82 | // p = p (r) = p_1 - \frac{q_1 \nu}{2 \pi k} \text{ln} (\frac{r}{r_1}), | ||
| 83 | // ``` | ||
| 84 | // | ||
| 85 | // where $`q_1`$ is the mass flux into the domain at the inner radius $`r_1`$ | ||
| 86 | // (in kg/s/m) and $`\nu = \mu/\varrho`$ is the kinematic viscosity. | ||
| 87 | // The following function evaluates this solution depending on the | ||
| 88 | // position in the domain. We use this function here both to specify Dirichlet | ||
| 89 | // boundaries and to evaluate the error of the numerical solutions obtained for | ||
| 90 | // different levels of grid refinement. | ||
| 91 | // [[codeblock]] | ||
| 92 | 6210 | PrimaryVariables exactSolution(const GlobalPosition& globalPos) const | |
| 93 | { | ||
| 94 | 6210 | const auto r = globalPos[0]; | |
| 95 | 6210 | const auto p = p1_ - 1.0/(2*M_PI)*nu_/k_*q1_*std::log(r/r1_); | |
| 96 | 6210 | return p; | |
| 97 | } | ||
| 98 | |||
| 99 | ✗ | const Scalar exactVelocity(const GlobalPosition& globalPos) const | |
| 100 | { | ||
| 101 | 3100 | const auto r = globalPos[0]; | |
| 102 | 3100 | const auto v = q1_/(2*M_PI)/rho_/r; | |
| 103 | ✗ | return v; | |
| 104 | } | ||
| 105 | |||
| 106 | private: | ||
| 107 | // private data members required for the analytical solution | ||
| 108 | Scalar q1_, k_, nu_, r1_, p1_, rho_; | ||
| 109 | }; | ||
| 110 | |||
| 111 | } // end namespace Dumux | ||
| 112 | // [[/codeblock]] | ||
| 113 | // [[/content]] | ||
| 114 | #endif | ||
| 115 |