diff --git a/src/callbacks_step/analysis_dg2d.jl b/src/callbacks_step/analysis_dg2d.jl index 4cd92ce7c5f..e089133fa17 100644 --- a/src/callbacks_step/analysis_dg2d.jl +++ b/src/callbacks_step/analysis_dg2d.jl @@ -279,30 +279,17 @@ end function analyze(::Val{:l2_divb}, du, u, t, mesh::TreeMesh{2}, - equations::IdealGlmMhdEquations2D, dg::DGSEM, cache) + equations, dg::DGSEM, cache) integrate_via_indices(u, mesh, equations, dg, cache, cache, dg.basis.derivative_matrix) do u, i, j, element, equations, dg, cache, derivative_matrix divb = zero(eltype(u)) for k in eachnode(dg) - divb += (derivative_matrix[i, k] * u[6, k, j, element] + - derivative_matrix[j, k] * u[7, i, k, element]) - end - divb *= cache.elements.inverse_jacobian[element] - divb^2 - end |> sqrt -end + B1_kj, _, _ = magnetic_field(u[:, k, j, element], equations) + _, B2_ik, _ = magnetic_field(u[:, i, k, element], equations) -function analyze(::Val{:l2_divb}, du, u, t, - mesh::TreeMesh{2}, equations::IdealGlmMhdMulticomponentEquations2D, - dg::DG, cache) - integrate_via_indices(u, mesh, equations, dg, cache, cache, - dg.basis.derivative_matrix) do u, i, j, element, equations, - dg, cache, derivative_matrix - divb = zero(eltype(u)) - for k in eachnode(dg) - divb += (derivative_matrix[i, k] * u[5, k, j, element] + - derivative_matrix[j, k] * u[6, i, k, element]) + divb += (derivative_matrix[i, k] * B1_kj + + derivative_matrix[j, k] * B2_ik) end divb *= cache.elements.inverse_jacobian[element] divb^2 @@ -312,7 +299,7 @@ end function analyze(::Val{:l2_divb}, du, u, t, mesh::Union{StructuredMesh{2}, UnstructuredMesh2D, P4estMesh{2}, T8codeMesh{2}}, - equations::IdealGlmMhdEquations2D, dg::DGSEM, cache) + equations, dg::DGSEM, cache) @unpack contravariant_vectors = cache.elements integrate_via_indices(u, mesh, equations, dg, cache, cache, dg.basis.derivative_matrix) do u, i, j, element, equations, @@ -323,10 +310,13 @@ function analyze(::Val{:l2_divb}, du, u, t, Ja21, Ja22 = get_contravariant_vector(2, contravariant_vectors, i, j, element) # Compute the transformed divergence for k in eachnode(dg) + B1_kj, B2_kj, _ = magnetic_field(u[:, k, j, element], equations) + B1_ik, B2_ik, _ = magnetic_field(u[:, i, k, element], equations) + divb += (derivative_matrix[i, k] * - (Ja11 * u[6, k, j, element] + Ja12 * u[7, k, j, element]) + + (Ja11 * B1_kj + Ja12 * B2_kj) + derivative_matrix[j, k] * - (Ja21 * u[6, i, k, element] + Ja22 * u[7, i, k, element])) + (Ja21 * B1_ik + Ja22 * B2_ik)) end divb *= cache.elements.inverse_jacobian[i, j, element] divb^2 @@ -335,7 +325,7 @@ end function analyze(::Val{:linf_divb}, du, u, t, mesh::TreeMesh{2}, - equations::IdealGlmMhdEquations2D, dg::DGSEM, cache) + equations, dg::DGSEM, cache) @unpack derivative_matrix, weights = dg.basis # integrate over all elements to get the divergence-free condition errors @@ -344,30 +334,11 @@ function analyze(::Val{:linf_divb}, du, u, t, for j in eachnode(dg), i in eachnode(dg) divb = zero(eltype(u)) for k in eachnode(dg) - divb += (derivative_matrix[i, k] * u[6, k, j, element] + - derivative_matrix[j, k] * u[7, i, k, element]) - end - divb *= cache.elements.inverse_jacobian[element] - linf_divb = max(linf_divb, abs(divb)) - end - end - - return linf_divb -end - -function analyze(::Val{:linf_divb}, du, u, t, - mesh::TreeMesh{2}, equations::IdealGlmMhdMulticomponentEquations2D, - dg::DG, cache) - @unpack derivative_matrix, weights = dg.basis + B1_kj, _, _ = magnetic_field(u[:, k, j, element], equations) + _, B2_ik, _ = magnetic_field(u[:, i, k, element], equations) - # integrate over all elements to get the divergence-free condition errors - linf_divb = zero(eltype(u)) - for element in eachelement(dg, cache) - for j in eachnode(dg), i in eachnode(dg) - divb = zero(eltype(u)) - for k in eachnode(dg) - divb += (derivative_matrix[i, k] * u[5, k, j, element] + - derivative_matrix[j, k] * u[6, i, k, element]) + divb += (derivative_matrix[i, k] * B1_kj + + derivative_matrix[j, k] * B2_ik) end divb *= cache.elements.inverse_jacobian[element] linf_divb = max(linf_divb, abs(divb)) @@ -380,7 +351,7 @@ end function analyze(::Val{:linf_divb}, du, u, t, mesh::Union{StructuredMesh{2}, UnstructuredMesh2D, P4estMesh{2}, T8codeMesh{2}}, - equations::IdealGlmMhdEquations2D, dg::DGSEM, cache) + equations, dg::DGSEM, cache) @unpack derivative_matrix, weights = dg.basis @unpack contravariant_vectors = cache.elements @@ -396,10 +367,13 @@ function analyze(::Val{:linf_divb}, du, u, t, element) # Compute the transformed divergence for k in eachnode(dg) + B1_kj, B2_kj, _ = magnetic_field(u[:, k, j, element], equations) + B1_ik, B2_ik, _ = magnetic_field(u[:, i, k, element], equations) + divb += (derivative_matrix[i, k] * - (Ja11 * u[6, k, j, element] + Ja12 * u[7, k, j, element]) + + (Ja11 * B1_kj + Ja12 * B2_kj) + derivative_matrix[j, k] * - (Ja21 * u[6, i, k, element] + Ja22 * u[7, i, k, element])) + (Ja21 * B1_ik + Ja22 * B2_ik)) end divb *= cache.elements.inverse_jacobian[i, j, element] linf_divb = max(linf_divb, abs(divb)) diff --git a/src/callbacks_step/analysis_dg3d.jl b/src/callbacks_step/analysis_dg3d.jl index 85880380c61..3c9c3a69f5e 100644 --- a/src/callbacks_step/analysis_dg3d.jl +++ b/src/callbacks_step/analysis_dg3d.jl @@ -307,16 +307,20 @@ function analyze(::typeof(entropy_timederivative), du, u, t, end function analyze(::Val{:l2_divb}, du, u, t, - mesh::TreeMesh{3}, equations::IdealGlmMhdEquations3D, + mesh::TreeMesh{3}, equations, dg::DGSEM, cache) integrate_via_indices(u, mesh, equations, dg, cache, cache, dg.basis.derivative_matrix) do u, i, j, k, element, equations, dg, cache, derivative_matrix divb = zero(eltype(u)) for l in eachnode(dg) - divb += (derivative_matrix[i, l] * u[6, l, j, k, element] + - derivative_matrix[j, l] * u[7, i, l, k, element] + - derivative_matrix[k, l] * u[8, i, j, l, element]) + B_ljk = magnetic_field(u[:, l, j, k, element], equations) + B_ilk = magnetic_field(u[:, i, l, k, element], equations) + B_ijl = magnetic_field(u[:, i, j, l, element], equations) + + divb += (derivative_matrix[i, l] * B_ljk[1] + + derivative_matrix[j, l] * B_ilk[2] + + derivative_matrix[k, l] * B_ijl[3]) end divb *= cache.elements.inverse_jacobian[element] divb^2 @@ -325,7 +329,7 @@ end function analyze(::Val{:l2_divb}, du, u, t, mesh::Union{StructuredMesh{3}, P4estMesh{3}, T8codeMesh{3}}, - equations::IdealGlmMhdEquations3D, + equations, dg::DGSEM, cache) @unpack contravariant_vectors = cache.elements integrate_via_indices(u, mesh, equations, dg, cache, cache, @@ -341,15 +345,16 @@ function analyze(::Val{:l2_divb}, du, u, t, element) # Compute the transformed divergence for l in eachnode(dg) + B_ljk = magnetic_field(u[:, l, j, k, element], equations) + B_ilk = magnetic_field(u[:, i, l, k, element], equations) + B_ijl = magnetic_field(u[:, i, j, l, element], equations) + divb += (derivative_matrix[i, l] * - (Ja11 * u[6, l, j, k, element] + Ja12 * u[7, l, j, k, element] + - Ja13 * u[8, l, j, k, element]) + + (Ja11 * B_ljk[1] + Ja12 * B_ljk[2] + Ja13 * B_ljk[3]) + derivative_matrix[j, l] * - (Ja21 * u[6, i, l, k, element] + Ja22 * u[7, i, l, k, element] + - Ja23 * u[8, i, l, k, element]) + + (Ja21 * B_ilk[1] + Ja22 * B_ilk[2] + Ja23 * B_ilk[3]) + derivative_matrix[k, l] * - (Ja31 * u[6, i, j, l, element] + Ja32 * u[7, i, j, l, element] + - Ja33 * u[8, i, j, l, element])) + (Ja31 * B_ijl[1] + Ja32 * B_ijl[2] + Ja33 * B_ijl[3])) end divb *= cache.elements.inverse_jacobian[i, j, k, element] divb^2 @@ -357,7 +362,7 @@ function analyze(::Val{:l2_divb}, du, u, t, end function analyze(::Val{:linf_divb}, du, u, t, - mesh::TreeMesh{3}, equations::IdealGlmMhdEquations3D, + mesh::TreeMesh{3}, equations, dg::DGSEM, cache) @unpack derivative_matrix, weights = dg.basis @@ -367,9 +372,13 @@ function analyze(::Val{:linf_divb}, du, u, t, for k in eachnode(dg), j in eachnode(dg), i in eachnode(dg) divb = zero(eltype(u)) for l in eachnode(dg) - divb += (derivative_matrix[i, l] * u[6, l, j, k, element] + - derivative_matrix[j, l] * u[7, i, l, k, element] + - derivative_matrix[k, l] * u[8, i, j, l, element]) + B_ljk = magnetic_field(u[:, l, j, k, element], equations) + B_ilk = magnetic_field(u[:, i, l, k, element], equations) + B_ijl = magnetic_field(u[:, i, j, l, element], equations) + + divb += (derivative_matrix[i, l] * B_ljk[1] + + derivative_matrix[j, l] * B_ilk[2] + + derivative_matrix[k, l] * B_ijl[3]) end divb *= cache.elements.inverse_jacobian[element] linf_divb = max(linf_divb, abs(divb)) @@ -386,7 +395,7 @@ end function analyze(::Val{:linf_divb}, du, u, t, mesh::Union{StructuredMesh{3}, P4estMesh{3}, T8codeMesh{3}}, - equations::IdealGlmMhdEquations3D, + equations, dg::DGSEM, cache) @unpack derivative_matrix, weights = dg.basis @unpack contravariant_vectors = cache.elements @@ -405,12 +414,16 @@ function analyze(::Val{:linf_divb}, du, u, t, k, element) # Compute the transformed divergence for l in eachnode(dg) - divb += (derivative_matrix[i, l] * (Ja11 * u[6, l, j, k, element] + - Ja12 * u[7, l, j, k, element] + Ja13 * u[8, l, j, k, element]) + - derivative_matrix[j, l] * (Ja21 * u[6, i, l, k, element] + - Ja22 * u[7, i, l, k, element] + Ja23 * u[8, i, l, k, element]) + - derivative_matrix[k, l] * (Ja31 * u[6, i, j, l, element] + - Ja32 * u[7, i, j, l, element] + Ja33 * u[8, i, j, l, element])) + B_ljk = magnetic_field(u[:, l, j, k, element], equations) + B_ilk = magnetic_field(u[:, i, l, k, element], equations) + B_ijl = magnetic_field(u[:, i, j, l, element], equations) + + divb += (derivative_matrix[i, l] * (Ja11 * B_ljk[1] + + Ja12 * B_ljk[2] + Ja13 * B_ljk[3]) + + derivative_matrix[j, l] * (Ja21 * B_ilk[1] + + Ja22 * B_ilk[2] + Ja23 * B_ilk[3]) + + derivative_matrix[k, l] * (Ja31 * B_ijl[1] + + Ja32 * B_ijl[2] + Ja33 * B_ijl[3])) end divb *= cache.elements.inverse_jacobian[i, j, k, element] linf_divb = max(linf_divb, abs(divb)) diff --git a/src/equations/ideal_glm_mhd_2d.jl b/src/equations/ideal_glm_mhd_2d.jl index 9383fdbe961..ba362525228 100644 --- a/src/equations/ideal_glm_mhd_2d.jl +++ b/src/equations/ideal_glm_mhd_2d.jl @@ -46,6 +46,9 @@ function default_analysis_integrals(::IdealGlmMhdEquations2D) (entropy_timederivative, Val(:l2_divb), Val(:linf_divb)) end +# Helper function to extract the magnetic field vector from the conservative variables +magnetic_field(u, equations::IdealGlmMhdEquations2D) = SVector(u[6], u[7], u[8]) + # Set initial conditions at physical location `x` for time `t` """ initial_condition_constant(x, t, equations::IdealGlmMhdEquations2D) diff --git a/src/equations/ideal_glm_mhd_3d.jl b/src/equations/ideal_glm_mhd_3d.jl index 8d7d0461398..d8c859b7a8a 100644 --- a/src/equations/ideal_glm_mhd_3d.jl +++ b/src/equations/ideal_glm_mhd_3d.jl @@ -44,6 +44,9 @@ function default_analysis_integrals(::IdealGlmMhdEquations3D) (entropy_timederivative, Val(:l2_divb), Val(:linf_divb)) end +# Helper function to extract the magnetic field vector from the conservative variables +magnetic_field(u, equations::IdealGlmMhdEquations3D) = SVector(u[6], u[7], u[8]) + # Set initial conditions at physical location `x` for time `t` """ initial_condition_constant(x, t, equations::IdealGlmMhdEquations3D) diff --git a/src/equations/ideal_glm_mhd_multicomponent_2d.jl b/src/equations/ideal_glm_mhd_multicomponent_2d.jl index 99fe391301d..509a2507cd9 100644 --- a/src/equations/ideal_glm_mhd_multicomponent_2d.jl +++ b/src/equations/ideal_glm_mhd_multicomponent_2d.jl @@ -101,6 +101,10 @@ function default_analysis_integrals(::IdealGlmMhdMulticomponentEquations2D) (entropy_timederivative, Val(:l2_divb), Val(:linf_divb)) end +# Helper function to extract the magnetic field vector from the conservative variables +magnetic_field(u, equations::IdealGlmMhdMulticomponentEquations2D) = SVector(u[5], u[6], + u[7]) + """ initial_condition_convergence_test(x, t, equations::IdealGlmMhdMulticomponentEquations2D)