16 × 16 × 29 ×3 M_{x} M_{y} M_{z} M_{ρ}

U = (R, M_{x}, M_{y}, M_{z}, E)^{T} ,  (1)

F^{x} = (Rv^{x}, M_{x}v^{x} + p, M_{y}v^{y}, M_{z}v^{z}, (E + p)v^{x})^{T} ,  (2)

F^{y} = (Rv^{y}, M_{x}v^{x}, M_{y}v^{y} + p, M_{z}v^{z}, (E + p)v^{y})^{T} ,  (3)

F^{z} = (Rv^{z}, M_{x}v^{x}, M_{y}v^{y}, M_{z}v^{z} + p, (E + p)v^{z})^{T} ,  (4)

\frac{∂U}{∂t} + \frac{∂}{∂x}(F^{x}) + \frac{∂}{∂y} (F^{y}) + \frac{∂}{∂z} (F^{z}) = 0.  (5)

p = (Γ − 1)(e − n).

U^{n+1}_{i} = U^{n}_{i} − \frac{δt}{δx}(F_{i+ \frac{1}{2}} − F_{i− \frac{1}{2}} ).  (6)

U_{i} U_{i+1} F_{i+ \frac{1}{2}} i + \frac{1}{2} c_{s}

R = γn,  (7)

M^{x} = γ^{2}(e + p)v^{x},  (8)

M^{y} = γ^{2}(e + p)v^{y},  (9)

M^{z} = γ^{2}(e + p)v^{z},  (10)

E = γ^{2}(e + p) − p,  (11)

γ = (1 − v^{2})^{−1/2} v^{2} = (v^{x})^{2} + (v^{y})^{2} + (v^{z})^{2} v^{x} v^{y} v^{z} [Γv (E − Mv) − M (1 − v^{2})]^{2}

− (1 − v^{2}) v^{2} (Γ − 1)^{2} R^{2} = 0,  (12)

M^{2} = (M^{x})^{2} + (M^{y})^{2} + (M^{z})^{2}