Patent ID: 8805655

Claim:
A computer implemented method for simulating two-dimensional inviscid subsonic flows, comprising the following steps: (1) Transforming, by using a computer, a set of two-dimensional unsteady Euler equations in a Euler plane into a set of unsteady Euler equations in Lagrangian formulation in a Lagrangian plane, which has one time coordinate direction stated by a Lagrangian time τ and two space coordinate directions stated by a stream function ξ and a Lagrangian-distance λ, through a transforming matrix J = [ 1 0 0 hu cos ⁢ ⁢ θ U hv sin ⁢ ⁢ θ V ] ; said unsteady Euler equations in Lagrangian formulation include two set equations: a set of Lagrangian physical conservation equations and a set of geometric conservation equations, which formally are written as: the Lagrangian physical conservation equations ∂ f L ∂ τ + ∂ F L ∂ λ + ∂ G L ∂ ξ = 0 , where f L is the conservation variables vector and F L , G L are the convective fluxes respectively in the λ and ξ direction in the Lagrangian plane, in detailed f L = [ ρ ⁢ ⁢ J ρ ⁢ ⁢ Ju ρ ⁢ ⁢ Jv ρ ⁢ ⁢ JE ] , F L = [ ( 1 - h ) ⁢ ρ ⁢ ⁢ K ( 1 - h ) ⁢ ρ ⁢ ⁢ Ku + Vp ( 1 - h ) ⁢ ρ ⁢ ⁢ Kv - Up ( 1 - h ) ⁢ ρ ⁢ ⁢ KH ] , G L = [ 0 - p ⁢ ⁢ sin ⁢ ⁢ θ p ⁢ ⁢ cos ⁢ ⁢ θ 0 ] , θ = tg - 1 ⁡ ( v u ) , K=uV −vU, 0 <h≦ 1; the geometric conservation equations ∂ f g ∂ τ + ∂ F g ∂ λ + ∂ G g ∂ ξ = 0 , ⁢ where ⁢ ⁢ f g = [ U V ] , F g = [ 0 0 ] , G g = [ - hu - hv ] . in all above, the variables t, ρ, p, E and H are respectively the time, fluid density, pressure, total energy and enthalpy; u, v are the Cartesian components of flow velocity V, and U, V are the Lagrangian geometry state variables; (2) reading object geometry for providing points on a surface of an object; (3) establishing a computing mesh around said object; (4) using a Strang-dimensional-splitting scheme with hybrid upwind flux operators solving the unsteady Euler equations in Lagrangian formulation in the Lagrangian plane.