@@ -11,7 +11,7 @@ Centered finite difference scheme for first order derivative at grid point `I`
1111along dimension `dim`.
1212"""
1313function D⁰ (ϕ:: CartesianMeshField , I, dim)
14- h = meshsize (ϕ, dim)
14+ h = meshsize (ϕ, dim)
1515 Im = _decrement_index (I, dim)
1616 Ip = _increment_index (I, dim)
1717 return (ϕ[Ip] - ϕ[Im]) / (2 h)
@@ -24,14 +24,14 @@ Forward finite difference scheme for first order derivative at grid point `I`
2424along dimension `dim`.
2525"""
2626@inline function D⁺ (ϕ:: CartesianMeshField , I, dim)
27- h = meshsize (ϕ, dim)
27+ h = meshsize (ϕ, dim)
2828 Ip = _increment_index (I, dim)
2929 return (ϕ[Ip] - ϕ[I]) / h
3030end
3131
3232function D⁺⁺ (ϕ:: CartesianMeshField , I, dim)
33- h = meshsize (ϕ, dim)
34- Ip = _increment_index (I, dim)
33+ h = meshsize (ϕ, dim)
34+ Ip = _increment_index (I, dim)
3535 Ipp = _increment_index (I, dim, 2 )
3636 return (- 1.5 * ϕ[I] + 2 * ϕ[Ip] - 1 / 2 * ϕ[Ipp]) / h
3737end
@@ -43,7 +43,7 @@ Backward finite difference scheme for first order derivative at grid point `I`
4343along dimension `dim`.
4444"""
4545function D⁻ (ϕ:: CartesianMeshField , I, dim)
46- h = meshsize (ϕ, dim)
46+ h = meshsize (ϕ, dim)
4747 Im = _decrement_index (I, dim)
4848 return (ϕ[I] - ϕ[Im]) / h
4949end
5757
5858function weno5⁻ (ϕ:: CartesianMeshField , I, dim)
5959 # see section 3.4 of Osher-Fedwik
60- Im = _decrement_index (I, dim)
60+ Im = _decrement_index (I, dim)
6161 Imm = _decrement_index (Im, dim)
62- Ip = _increment_index (I, dim)
62+ Ip = _increment_index (I, dim)
6363 Ipp = _increment_index (Ip, dim)
6464 # finite differences
6565 v1 = D⁻ (ϕ, Imm, dim)
@@ -76,7 +76,7 @@ function weno5⁻(ϕ::CartesianMeshField, I, dim)
7676 S2 = (13 / 12 ) * (v2 - 2 * v3 + v4)^ 2 + (1 / 4 ) * (v2 - v4)^ 2
7777 S3 = (13 / 12 ) * (v3 - 2 * v4 + v5)^ 2 + (1 / 4 ) * (3 * v3 - 4 * v4 + v5)^ 2
7878 # fudge factor
79- ϵ = 1e -6 * max (v1^ 2 , v2^ 2 , v3^ 2 , v4^ 2 , v5^ 2 ) + 1e -99
79+ ϵ = 1.0e -6 * max (v1^ 2 , v2^ 2 , v3^ 2 , v4^ 2 , v5^ 2 ) + 1.0e -99
8080 # weights
8181 α1 = 0.1 / (S1 + ϵ)^ 2
8282 α2 = 0.6 / (S2 + ϵ)^ 2
9090
9191function weno5⁺ (ϕ:: CartesianMeshField , I, dim)
9292 # see section 3.4 of Osher-Fedwik
93- Im = _decrement_index (I, dim)
93+ Im = _decrement_index (I, dim)
9494 Imm = _decrement_index (Im, dim)
95- Ip = _increment_index (I, dim)
95+ Ip = _increment_index (I, dim)
9696 Ipp = _increment_index (Ip, dim)
9797 # finite differences
9898 v1 = D⁺ (ϕ, Ipp, dim)
@@ -109,7 +109,7 @@ function weno5⁺(ϕ::CartesianMeshField, I, dim)
109109 S2 = (13 / 12 ) * (v2 - 2 * v3 + v4)^ 2 + (1 / 4 ) * (v2 - v4)^ 2
110110 S3 = (13 / 12 ) * (v3 - 2 * v4 + v5)^ 2 + (1 / 4 ) * (3 * v3 - 4 * v4 + v5)^ 2
111111 # fudge factor
112- ϵ = 1e -6 * max (v1^ 2 , v2^ 2 , v3^ 2 , v4^ 2 , v5^ 2 ) + 1e -99
112+ ϵ = 1.0e -6 * max (v1^ 2 , v2^ 2 , v3^ 2 , v4^ 2 , v5^ 2 ) + 1.0e -99
113113 # weights
114114 α1 = 0.1 / (S1 + ϵ)^ 2
115115 α2 = 0.6 / (S2 + ϵ)^ 2
@@ -128,7 +128,7 @@ Centered finite difference scheme for second order derivative at grid point `I`
128128along dimension `dim`. E.g. if `dim=1`, this approximates `∂ₓₓ`.
129129"""
130130function D2⁰ (ϕ:: CartesianMeshField , I, dim)
131- h = meshsize (ϕ, dim)
131+ h = meshsize (ϕ, dim)
132132 Im = _decrement_index (I, dim)
133133 Ip = _increment_index (I, dim)
134134 return (ϕ[Ip] - 2 ϕ[I] + ϕ[Im]) / h^ 2
@@ -143,7 +143,7 @@ along the dimensions `dims`.
143143If `dims[1] == dims[2]`, it is more efficient to call `D2⁰(ϕ,I,dims[1])`.
144144"""
145145function D2 (ϕ, I, dims)
146- h = meshsize (ϕ)
146+ h = meshsize (ϕ)
147147 Ip = _increment_index (I, dims[1 ])
148148 Im = _decrement_index (I, dims[1 ])
149149 return (D⁰ (ϕ, Ip, dims[2 ]) - D⁰ (ϕ, Im, dims[2 ])) / (2 * h[dims[1 ]])
@@ -156,8 +156,8 @@ Upward finite difference scheme for second order derivative at grid point `I`
156156along dimension `dim`. E.g. if `dim=1`, this approximates `∂ₓₓ`.
157157"""
158158function D2⁺⁺ (ϕ:: CartesianMeshField , I, dim)
159- h = meshsize (ϕ, dim)
160- Ip = _increment_index (I, dim, 1 )
159+ h = meshsize (ϕ, dim)
160+ Ip = _increment_index (I, dim, 1 )
161161 Ipp = _increment_index (I, dim, 2 )
162162 return (ϕ[I] - 2 ϕ[Ip] + ϕ[Ipp]) / h^ 2
163163end
@@ -169,8 +169,8 @@ Backward finite difference scheme for second order derivative at grid point `I`
169169along dimension `dim`. E.g. if `dim=1`, this approximates `∂ₓₓ`.
170170"""
171171function D2⁻⁻ (ϕ:: CartesianMeshField , I, dim)
172- h = meshsize (ϕ, dim)
173- Im = _decrement_index (I, dim, 1 )
172+ h = meshsize (ϕ, dim)
173+ Im = _decrement_index (I, dim, 1 )
174174 Imm = _decrement_index (I, dim, 2 )
175175 return (ϕ[Imm] - 2 ϕ[Im] + ϕ[I]) / h^ 2
176176end
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