Hyperbolic Quadrature Method of Moments for the One-Dimensional Kinetic Equation

A tractable solution is proposed to a classical problem in kinetic theory, namely, given any set of realizable velocity moments up order $2n$, closure for the moment $2n+1$ constructed which system found from free-transport term one-dimensional (1-D) equation globally hyperbolic and conservative form. In prior work, quadrature method (HyQMOM) was introduced close this fourth ($n \le 2$). Here, HyQMOM reformulated extended arbitrary even-order moments. The defined based on properties monic orthogonal polynomials $Q_n$ that are uniquely by $2n-1$. Thus, strictly does not rely reconstruction distribution function with same On boundary space, $n$ double roots characteristic polynomial $P_{2n+1}$ Jacobian matrix $Q_n$, while interior, share roots. remaining $n+1$ bound separate $Q_n$. An efficient algorithm, Chebyshev computing $2n$ developed. analytical 1-D Riemann used demonstrate convergence increasing $n$.