Linear Moment Models to Approximate Knudsen Layers

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As reduction of Boltzmann equation, equations are available to model Knudsen layers near solid wall, where proper conditions should be prescribed. Utilizing an orthogonal decomposition, we separate part with damping term from and then impose new class on it. Due condition, show that half-space value problem admits unique solution explicit expressions. Instantly, well-posedness is achieved. apply procedure classical flow problems Shakhov collision term, such as velocity slip temperature jump problems. The can capture very high accuracy using only few moments.