Local integral method for computing molecular diffusion and chemical reaction

Claim 1

A computer program embodied on a computer-readable medium for determining molecular diffusion and chemical reaction within a material by determining species concentrations and reaction rates of nonequilibrium combustion in a turbulent reacting flow, the improvement comprising: linearly separating a velocity field of the turbulent reacting flow into a curl-free part and a divergence-free part; tracking the divergence-free part of the turbulent reacting flow by solving, at a plurality of first points on a first material surface, a first parabolized form of a first differential equation reduced from and approximating a more complex governing first partial differential equation; treating as negligible the curl-free part of the turbulent reacting flow; determining a shape deformation value of a second material surface over time as a function of the tracked divergence-free part; determining a rate of stretch of the second material surface as a function of the shape deformation value; relating the rate of stretch to mixing of at least one conserved scalar quantity in the turbulent reacting flow by solving, at a plurality of second points on the second material surface, a second parabolized form of a second differential equation reduced from and approximating a more complex governing second partial differential equation; determining a gradient field of conserved scalars in the turbulent reacting flow as a function of the second solved differential equation; calculating conserved scalar values from the gradient field of conserved scalars; and determining a species concentration and a reaction rate of the nonequilibrium combustion by correlating the calculated conserved scalar values and the determined gradient field of conserved scalars with corresponding values of a flamelet library.