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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,128 @@ | ||
| ############################################################################## | ||
| # ACAUSAL | ||
| ############################################################################## | ||
|
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||
| export AlgebraicModel | ||
| export structural_solve | ||
| export perfect_gas_constants | ||
| export perfect_gas_model | ||
|
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||
| ############################################################################## | ||
| # EXCEPTIONS | ||
| ############################################################################## | ||
|
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| struct UnsolvableAlgebraicModel <: Exception | ||
| msg::String | ||
|
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| function UnsolvableAlgebraicModel(vars, pars) | ||
| svars, spars = join(vars, ", "), join(pars, ", ") | ||
|
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| return new( | ||
| "Unable to solve algebraic model containing [$(svars)] " * | ||
| "by providing only [$(spars)]! Please, revise the " * | ||
| "setup of the system!" | ||
| ) | ||
| end | ||
| end | ||
|
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| function Base.showerror(io::IO, err::UnsolvableAlgebraicModel) | ||
| print(io, "UnsolvableAlgebraicModel: ") | ||
| print(io, err.msg) | ||
| end | ||
|
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| ############################################################################## | ||
| # ALGEBRAIC MODEL | ||
| ############################################################################## | ||
|
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| struct AlgebraicModel | ||
| vars::NamedTuple | ||
| eqns::Vector{Equation} | ||
| pars::Dict{Symbol, Float64} | ||
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| function AlgebraicModel(vars, eqns, pars) | ||
| vars = Dict(map(v->(Symbol(v), v), vars)) | ||
| return new(tuplefy(vars), eqns, pars) | ||
| end | ||
| end | ||
|
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| function structural_solve(obj::AlgebraicModel) | ||
| eqns = replacement_solve(obj) | ||
|
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| if has_pars(obj) && has_dofs(obj, eqns) | ||
| throw(UnsolvableAlgebraicModel(obj.vars, obj.pars)) | ||
| end | ||
|
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| @mtkbuild ns = NonlinearSystem(eqns, [values(obj.vars)...], []) | ||
| sol = solve(NonlinearProblem(ns, [], [])) | ||
|
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| solved_for = map(e->e.lhs, observed(ns)) | ||
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| pars = tuplefy(obj.pars) | ||
| vars = NamedTuple(map(n->(Symbol(n), sol[n]), solved_for)) | ||
| return merge(pars, vars) | ||
| end | ||
|
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| function replacement_solve(obj::AlgebraicModel) | ||
| # Retrieve names provided in object `pars` (parameters). | ||
| subs = map(v->(v, get(obj.pars, Symbol(v), v)), values(obj.vars)) | ||
|
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| # Replace at once all identified symbols for solving. | ||
| return substitute(obj.eqns, Dict(subs)) | ||
| end | ||
|
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| function has_pars(obj::AlgebraicModel) | ||
| return length(obj.pars) > 0 | ||
| end | ||
|
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| function has_dofs(obj::AlgebraicModel, eqns) | ||
| return length(obj.vars) - length(obj.pars) != length(eqns) | ||
| end | ||
|
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| ############################################################################## | ||
| # APPLICATIONS | ||
| ############################################################################## | ||
|
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| function perfect_gas_constants(; pars...) | ||
| vars = @variables begin | ||
| k, [bounds = (1, Inf)] | ||
| R, [bounds = (0, Inf)] | ||
| cp, [bounds = (0, Inf)] | ||
| cv, [bounds = (0, Inf)] | ||
| end | ||
|
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| eqns = [ | ||
| 0 ~ cp - k * cv, | ||
| 0 ~ cv - R / (k - 1) | ||
| ] | ||
|
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| return AlgebraicModel(vars, eqns, pars) | ||
| end | ||
|
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| function perfect_gas_model(; pars...) | ||
| model = perfect_gas_constants(;) | ||
|
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| vars = @variables begin | ||
| p, [bounds = (0, Inf)] | ||
| ρ, [bounds = (0, Inf)] | ||
| T, [bounds = (0, Inf)] | ||
| h, [bounds = (0, Inf)] | ||
| s, [bounds = (0, Inf)] | ||
| end | ||
|
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| R = model.vars.R | ||
| cp = model.vars.cp | ||
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| vars = [vars..., values(model.vars)...] | ||
| eqns = [ | ||
| 0 ~ p - ρ * R * T, | ||
| 0 ~ h - cp * T, | ||
| 0 ~ s - cp * log(T) + R * log(p), | ||
| model.eqns... | ||
| ] | ||
|
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| return AlgebraicModel(vars, eqns, pars) | ||
| end | ||
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| ############################################################################## | ||
| # EOF | ||
| ############################################################################## |