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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/utils/euler-manufactured.jl
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#= Usage:

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# Start Julia

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julia --color=yes

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# Install Reduce.jl package (only necessary once)

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import Pkg; Pkg.add("Reduce");

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# Load file

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julia> using Revise

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julia> includet("euler-manufactured.jl")

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# Run methods to generate source terms. The source terms that need to be

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# implemented can be found in the `source_...` variables of the quote'd output.

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# If you want, you can also modify, e.g., the ini method to get different manufactured solutions.

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julia> euler1d()

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julia> euler2d()

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julia> euler3d()

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=#

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using Reduce

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@force using Reduce.Algebra

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# Original Reduce code (CompressibleEulerEquations 1D)

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#=

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clear(γ,f,A,ω,c,ini,rho,rho_v1,rho_v2,rho_v3,rho_e,v1,v2,p,x,y,t,u1,u2,u3,u4);

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ini := c + A * sin(ω * (x - t));

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rho := ini;

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rho_v1 := ini;

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rho_e := ini^2;

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v1 := rho_v1 / rho;

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p := (γ - 1) * (rho_e - 1/2 * rho * v1^2);

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source_rho    := df(rho, t)    + df(rho_v1, x)

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source_rho_v1 := df(rho_v1, t) + df(rho * v1^2 + p, x)

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source_rho_e  := df(rho_e, t)  + df((rho_e + p) * v1, x)

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=#

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function euler1d()

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    quote

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        ini = c + a * sin(ω * (x - t))

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        rho = ini

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        rho_v1 = ini

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        rho_e = ini^2

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        v1 = rho_v1 / rho

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        p = (γ - 1) * (rho_e - 1 / 2 * rho * v1^2)

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        #! format: off

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        source_rho    = df(rho, t)    + df(rho_v1, x)

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        source_rho_v1 = df(rho_v1, t) + df(rho * v1^2 + p, x)

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        source_rho_e  = df(rho_e, t)  + df((rho_e + p) * v1, x)

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        #! format: on

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    end |> rcall

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end

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# Original Reduce code (CompressibleEulerEquations 2D)

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#=

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clear(γ,f,A,ω,c,ini,rho,rho_v1,rho_v2,rho_v3,rho_e,v1,v2,p,x,y,t,u1,u2,u3,u4);

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ini := c + A * sin(ω * (x + y - t));

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rho := ini;

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rho_v1 := ini;

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rho_v2 := ini;

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rho_e := ini^2;

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v1 := rho_v1 / rho;

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v2 := rho_v2 / rho;

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p := (γ - 1) * (rho_e - 1/2 * rho * (v1^2 + v2^2));

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source_rho    := df(rho, t)    + df(rho_v1, x)           + df(rho_v2, y);

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source_rho_v1 := df(rho_v1, t) + df(rho * v1^2 + p, x)   + df(rho * v1 * v2, y);

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source_rho_v2 := df(rho_v2, t) + df(rho * v1 * v2, x)    + df(rho * v2^2 + p, y);

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source_rho_e  := df(rho_e, t)  + df((rho_e + p) * v1, x) + df((rho_e + p) * v2, y);

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=#

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function euler2d()

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    quote

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        ini = c + a * sin(ω * (x + y - t))

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        rho = ini

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        rho_v1 = ini

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        rho_v2 = ini

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        rho_e = ini^2

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        v1 = rho_v1 / rho

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        v2 = rho_v2 / rho

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        p = (γ - 1) * (rho_e - 1 / 2 * rho * (v1^2 + v2^2))

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        #! format: off

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        source_rho    = df(rho, t)    + df(rho_v1, x)           + df(rho_v2, y)

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        source_rho_v1 = df(rho_v1, t) + df(rho * v1^2 + p, x)   + df(rho * v1 * v2, y)

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        source_rho_v2 = df(rho_v2, t) + df(rho * v1 * v2, x)    + df(rho * v2^2 + p, y)

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        source_rho_e  = df(rho_e, t)  + df((rho_e + p) * v1, x) + df((rho_e + p) * v2, y)

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        #! format: on

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    end |> rcall

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end

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# Original Reduce code (CompressibleEulerEquations 3D)

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#=

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clear(γ,f,A,ω,c,a1,a2,a3,ini,rho,rho_v1,rho_v2,rho_v3,rho_e,v1,v2,v3,p,x,y,z,t);

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ini := c + A * sin(ω * (x + y + z - t));

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rho := ini;

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rho_v1 := ini;

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rho_v2 := ini;

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rho_v3 := ini;

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rho_e := ini^2;

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v1 := rho_v1 / rho;

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v2 := rho_v2 / rho;

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v3 := rho_v3 / rho;

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p := (γ - 1) * (rho_e - 1/2 * rho * (v1^2 + v2^2 + v3^2));

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source_rho    := df(rho, t)    + df(rho_v1, x)           + df(rho_v2, y)           + df(rho_v3, z);

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source_rho_v1 := df(rho_v1, t) + df(rho * v1^2 + p, x)   + df(rho * v1 * v2, y)    + df(rho * v1 * v3, z);

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source_rho_v2 := df(rho_v2, t) + df(rho * v1 * v2, x)    + df(rho * v2^2 + p, y)   + df(rho * v2 * v3, z);

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source_rho_v3 := df(rho_v3, t) + df(rho * v1 * v3, x)    + df(rho * v3 * v3, y)    + df(rho * v3^2 + p, z);

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source_rho_e  := df(rho_e, t)  + df((rho_e + p) * v1, x) + df((rho_e + p) * v2, y) + df((rho_e + p) * v3, z);

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=#

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function euler3d()

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    quote

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        ini = c + a * sin(ω * (x + y + z - t))

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        rho = ini

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        rho_v1 = ini

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        rho_v2 = ini

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        rho_v3 = ini

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        rho_e = ini^2

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        v1 = rho_v1 / rho

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        v2 = rho_v2 / rho

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        v3 = rho_v3 / rho

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        p = (γ - 1) * (rho_e - 1 / 2 * rho * (v1^2 + v2^2 + v3^2))

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        #! format: off

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        source_rho    = df(rho, t)    + df(rho_v1, x)           + df(rho_v2, y)           + df(rho_v3, z)

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        source_rho_v1 = df(rho_v1, t) + df(rho * v1^2 + p, x)   + df(rho * v1 * v2, y)    + df(rho * v1 * v3, z)

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        source_rho_v2 = df(rho_v2, t) + df(rho * v1 * v2, x)    + df(rho * v2^2 + p, y)   + df(rho * v2 * v3, z)

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        source_rho_v3 = df(rho_v3, t) + df(rho * v1 * v3, x)    + df(rho * v3 * v3, y)    + df(rho * v3^2 + p, z)

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        source_rho_e  = df(rho_e, t)  + df((rho_e + p) * v1, x) + df((rho_e + p) * v2, y) + df((rho_e + p) * v3, z)

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        #! format: on

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    end |> rcall

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end

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