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add references to semidiscretizations in docstrings (#128)
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JoshuaLampert authored Aug 9, 2024
1 parent 9dab98c commit 6577a58
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10 changes: 7 additions & 3 deletions src/equations/bbm_bbm_1d.jl
Original file line number Diff line number Diff line change
Expand Up @@ -12,11 +12,15 @@ The unknown quantities of the BBM-BBM equations are the total water height ``\et
The gravitational constant is denoted by `g` and the constant bottom topography (bathymetry) ``b = \eta_0 - D``. The water height above the bathymetry is therefore given by
``h = \eta - \eta_0 + D``. The BBM-BBM equations are only implemented for ``\eta_0 = 0``.
One reference for the BBM-BBM system can be found in
One reference for the BBM-BBM system can be found in Bona et al. (1998).
The semidiscretization implemented here conserves the mass and the energy and is developed in Ranocha et al. (2020).
- Jerry L. Bona, Min Chen (1998)
A Boussinesq system for two-way propagation of nonlinear dispersive waves
[DOI: 10.1016/S0167-2789(97)00249-2](https://doi.org/10.1016/S0167-2789(97)00249-2)
- Hendrik Ranocha, Dimitrios Mitsotakis, David I. Ketcheson (2020)
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
[DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119)
"""
struct BBMBBMEquations1D{RealT <: Real} <: AbstractBBMBBMEquations{1, 2}
gravity::RealT # gravitational constant
Expand Down Expand Up @@ -213,7 +217,7 @@ function rhs!(dq, q, t, mesh, equations::BBMBBMEquations1D, initial_condition,
return nothing
end

# Discretization that conserves the mass (for eta) and the energy for periodic boundary conditions, see
# Discretization that conserves the mass (for eta) and the energy for reflecting boundary conditions, see
# - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020)
# A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
# [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119)
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9 changes: 7 additions & 2 deletions src/equations/bbm_bbm_variable_bathymetry_1d.jl
Original file line number Diff line number Diff line change
Expand Up @@ -12,11 +12,16 @@ The unknown quantities of the BBM-BBM equations are the total water height ``\et
The gravitational constant is denoted by `g` and the bottom topography (bathymetry) ``b = \eta_0 - D``. The water height above the bathymetry is therefore given by
``h = \eta - \eta_0 + D``. The BBM-BBM equations are only implemented for ``\eta_0 = 0``.
One reference for the BBM-BBM system with spatially varying bathymetry can be found in
One reference for the BBM-BBM system with spatially varying bathymetry can be found in Israwi et al. (2022).
The semidiscretization implemented here conserves the mass and the energy, is well-balanced for the lake-at-rest state,
and is developed in Lampert and Ranocha (2024).
- Samer Israwi, Henrik Kalisch, Theodoros Katsaounis, Dimitrios Mitsotakis (2022)
A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis
[DOI: 10.1088/1361-6544/ac3c29](https://doi.org/10.1088/1361-6544/ac3c29)
- Joshua Lampert, Hendrik Ranocha (2024)
Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
[DOI: 10.48550/arXiv.2402.16669](https://doi.org/10.48550/arXiv.2402.16669)
"""
struct BBMBBMVariableEquations1D{RealT <: Real} <: AbstractBBMBBMEquations{1, 3}
gravity::RealT # gravitational constant
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13 changes: 10 additions & 3 deletions src/equations/svaerd_kalisch_1d.jl
Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
@doc raw"""
SvärdKalischEquations1D(gravity, eta0 = 1.0, alpha = 0.0, beta = 0.2308939393939394, gamma = 0.04034343434343434)
SvaerdKalischEquations1D(gravity, eta0 = 1.0, alpha = 0.0, beta = 0.2308939393939394, gamma = 0.04034343434343434)
Dispersive system by Svärd and Kalisch in one spatial dimension with spatially varying bathymetry. The equations are given in conservative variables by
```math
Expand All @@ -20,11 +20,18 @@ The unknown quantities of the Svärd-Kalisch equations are the total water heigh
The gravitational constant is denoted by `g` and the bottom topography (bathymetry) ``b = \eta_0 - D``. The water height above the bathymetry is therefore given by
``h = \eta - \eta_0 + D``.
The equations by Svärd and Kalisch are presented and analyzed in
`SvärdKalischEquations1D` is an alias for `SvaerdKalischEquations1D`.
The equations by Svärd and Kalisch are presented and analyzed in Svärd and Kalisch (2023).
The semidiscretization implemented here conserves the mass and the energy, is well-balanced for the lake-at-rest state,
and is developed in Lampert and Ranocha (2024).
- Magnus Svärd, Henrik Kalisch (2023)
A novel energy-bounded Boussinesq model and a well-balanced and stable numerical discretization
[arXiv: 2302.09924](https://arxiv.org/abs/2302.09924)
- Joshua Lampert, Hendrik Ranocha (2024)
Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
[DOI: 10.48550/arXiv.2402.16669](https://doi.org/10.48550/arXiv.2402.16669)
"""
struct SvaerdKalischEquations1D{RealT <: Real} <: AbstractSvaerdKalischEquations{1, 3}
gravity::RealT # gravitational constant
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