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Fixed cons2entropy files and implemented entropy2cons for `Compre…
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…ssibleEulerMulticomponent1D` and `CompressibleEulerMulticomponent2D` (#1767)

* initial bug fix

* formatting

* Added test cases for entropy2cons and cons2entropy for compressible multicomponent euler 1d and 2d

* Fixed total entropy function call

* minor typo

* Updated formatting

Co-authored-by: Jesse Chan <[email protected]>

* Updated formatting

Co-authored-by: Jesse Chan <[email protected]>

* Fixed formatting issues

* Update test/test_tree_1d_eulermulti.jl

* Update test/test_tree_2d_eulermulti.jl

---------

Co-authored-by: Jesse Chan <[email protected]>
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@teohyikhaw @jlchan
teohyikhaw and jlchan authored Dec 14, 2023
1 parent f191444 commit 40e1af4
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78 changes: 72 additions & 6 deletions src/equations/compressible_euler_multicomponent_1d.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -461,6 +461,7 @@ end
# Convert conservative variables to entropy
@inline function cons2entropy(u, equations::CompressibleEulerMulticomponentEquations1D)
@unpack cv, gammas, gas_constants = equations

rho_v1, rho_e = u

rho = density(u, equations)
Expand All @@ -480,21 +481,86 @@ end
s = log(p) - gamma * log(rho) - log(gas_constant)
rho_p = rho / p
T = (rho_e - 0.5 * rho * v_square) / (help1)
entrop_rho = SVector{ncomponents(equations), real(equations)}(gas_constant *
((gamma - s) /
(gamma - 1.0) -
(0.5 * v_square *
rho_p))

entrop_rho = SVector{ncomponents(equations), real(equations)}((cv[i] *
(1 - log(T)) +
gas_constants[i] *
(1 + log(u[i + 2])) -
v1^2 / (2 * T))
for i in eachcomponent(equations))

w1 = gas_constant * v1 * rho_p
w2 = gas_constant * (-1.0 * rho_p)
w2 = gas_constant * (-rho_p)

entrop_other = SVector{2, real(equations)}(w1, w2)

return vcat(entrop_other, entrop_rho)
end

# Convert entropy variables to conservative variables
@inline function entropy2cons(w, equations::CompressibleEulerMulticomponentEquations1D)
@unpack gammas, gas_constants, cv, cp = equations
T = -1 / w[2]
v1 = w[1] * T
cons_rho = SVector{ncomponents(equations), real(equations)}(exp(1 /
gas_constants[i] *
(-cv[i] *
log(-w[2]) -
cp[i] + w[i + 2] -
0.5 * w[1]^2 /
w[2]))
for i in eachcomponent(equations))

rho = zero(cons_rho[1])
help1 = zero(cons_rho[1])
help2 = zero(cons_rho[1])
p = zero(cons_rho[1])
for i in eachcomponent(equations)
rho += cons_rho[i]
help1 += cons_rho[i] * cv[i] * gammas[i]
help2 += cons_rho[i] * cv[i]
p += cons_rho[i] * gas_constants[i] * T
end
u1 = rho * v1
gamma = help1 / help2
u2 = p / (gamma - 1) + 0.5 * rho * v1^2
cons_other = SVector{2, real(equations)}(u1, u2)
return vcat(cons_other, cons_rho)
end

@inline function total_entropy(u, equations::CompressibleEulerMulticomponentEquations1D)
@unpack cv, gammas, gas_constants = equations
rho_v1, rho_e = u
rho = density(u, equations)
T = temperature(u, equations)

total_entropy = zero(u[1])
for i in eachcomponent(equations)
total_entropy -= u[i + 2] * (cv[i] * log(T) - gas_constants[i] * log(u[i + 2]))
end

return total_entropy
end

@inline function temperature(u, equations::CompressibleEulerMulticomponentEquations1D)
@unpack cv, gammas, gas_constants = equations

rho_v1, rho_e = u

rho = density(u, equations)
help1 = zero(rho)

for i in eachcomponent(equations)
help1 += u[i + 2] * cv[i]
end

v1 = rho_v1 / rho
v_square = v1^2
T = (rho_e - 0.5 * rho * v_square) / help1

return T
end

"""
totalgamma(u, equations::CompressibleEulerMulticomponentEquations1D)
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80 changes: 74 additions & 6 deletions src/equations/compressible_euler_multicomponent_2d.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -665,22 +665,57 @@ end
s = log(p) - gamma * log(rho) - log(gas_constant)
rho_p = rho / p
T = (rho_e - 0.5 * rho * v_square) / (help1)
entrop_rho = SVector{ncomponents(equations), real(equations)}(gas_constant *
((gamma - s) /
(gamma - 1.0) -
(0.5 * v_square *
rho_p))

entrop_rho = SVector{ncomponents(equations), real(equations)}((cv[i] *
(1 - log(T)) +
gas_constants[i] *
(1 + log(u[i + 3])) -
v_square / (2 * T))
for i in eachcomponent(equations))

w1 = gas_constant * v1 * rho_p
w2 = gas_constant * v2 * rho_p
w3 = gas_constant * rho_p * (-1)
w3 = gas_constant * (-rho_p)

entrop_other = SVector{3, real(equations)}(w1, w2, w3)

return vcat(entrop_other, entrop_rho)
end

# Convert entropy variables to conservative variables
@inline function entropy2cons(w, equations::CompressibleEulerMulticomponentEquations2D)
@unpack gammas, gas_constants, cp, cv = equations
T = -1 / w[3]
v1 = w[1] * T
v2 = w[2] * T
v_squared = v1^2 + v2^2
cons_rho = SVector{ncomponents(equations), real(equations)}(exp((w[i + 3] -
cv[i] *
(1 - log(T)) +
v_squared /
(2 * T)) /
gas_constants[i] -
1)
for i in eachcomponent(equations))

rho = zero(cons_rho[1])
help1 = zero(cons_rho[1])
help2 = zero(cons_rho[1])
p = zero(cons_rho[1])
for i in eachcomponent(equations)
rho += cons_rho[i]
help1 += cons_rho[i] * cv[i] * gammas[i]
help2 += cons_rho[i] * cv[i]
p += cons_rho[i] * gas_constants[i] * T
end
u1 = rho * v1
u2 = rho * v2
gamma = help1 / help2
u3 = p / (gamma - 1) + 0.5 * rho * v_squared
cons_other = SVector{3, real(equations)}(u1, u2, u3)
return vcat(cons_other, cons_rho)
end

# Convert primitive to conservative variables
@inline function prim2cons(prim, equations::CompressibleEulerMulticomponentEquations2D)
@unpack cv, gammas = equations
Expand All @@ -700,6 +735,39 @@ end
return vcat(cons_other, cons_rho)
end

@inline function total_entropy(u, equations::CompressibleEulerMulticomponentEquations2D)
@unpack cv, gammas, gas_constants = equations
rho = density(u, equations)
T = temperature(u, equations)

total_entropy = zero(u[1])
for i in eachcomponent(equations)
total_entropy -= u[i + 3] * (cv[i] * log(T) - gas_constants[i] * log(u[i + 3]))
end

return total_entropy
end

@inline function temperature(u, equations::CompressibleEulerMulticomponentEquations2D)
@unpack cv, gammas, gas_constants = equations

rho_v1, rho_v2, rho_e = u

rho = density(u, equations)
help1 = zero(rho)

for i in eachcomponent(equations)
help1 += u[i + 3] * cv[i]
end

v1 = rho_v1 / rho
v2 = rho_v2 / rho
v_square = v1^2 + v2^2
T = (rho_e - 0.5 * rho * v_square) / help1

return T
end

"""
totalgamma(u, equations::CompressibleEulerMulticomponentEquations2D)
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