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Co-authored-by: Hendrik Ranocha <[email protected]>
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JoshuaLampert and ranocha authored Aug 17, 2024
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9 changes: 6 additions & 3 deletions src/DispersiveShallowWater.jl
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DispersiveShallowWater
**DispersiveShallowWater.jl** is a Julia package that implements structure-preserving numerical methods for dispersive shallow water models.
It provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models.
It provides provably conservative, entropy-conserving, and well-balanced numerical schemes for some dispersive shallow water models.
The semidiscretizations are based on summation-by-parts (SBP) operators, which are implemented in SummationByPartsOperators.jl. To
obtain fully discrete schemes, the time integration methods from OrdinaryDiffEq.jl are used to solve the resulting ordinary differential equations.
The semidiscretizations are based on summation-by-parts (SBP) operators, which are implemented in
[SummationByPartsOperators.jl](https://github.com/ranocha/SummationByPartsOperators.jl). To
obtain fully discrete schemes, the time integration methods from
[OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl)
are used to solve the resulting ordinary differential equations.
Fully discrete entropy-conservative methods can be obtained by using the relaxation method provided by DispersiveShallowWater.jl.
See also: [DispersiveShallowWater.jl](https://github.com/JoshuaLampert/DispersiveShallowWater.jl)
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6 changes: 2 additions & 4 deletions src/equations/svaerd_kalisch_1d.jl
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Return the modified total energy of the primitive variables `q_global` for the
[`SvaerdKalischEquations1D`](@ref). It contains an additional term containing a
derivative compared to the usual `energy_total`. The `energy_total_modified`
is a conserved quantity of the Svärd-Kalisch equations.
The total energy is given by
derivative compared to the usual [`energy_total`](@ref). The `energy_total_modified`
is a conserved quantity of the Svärd-Kalisch equations given by
```math
\\frac{1}{2} g h^2 + \\frac{1}{2} h v^2 + \\frac{1}{2} \\hat\\beta v_x^2.
```
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