流動抵抗を無視した多要素解析における数値安定限界

抄録

It is valuable to develop a code to analyze Stirling engine performance in a high accuracy with a low calculation load. A program that solve at first assuming uniform pressure at every time, then adjust pressure distribution to satisfy pressure drop due to friction has such possibility. Such a program employing Runge-Kutta method, however, will become numerically unstable for a large time step. This prevents efficient calculation. This study made clear the stable time-step limit. It is employed as the stable condition that all absolute of eigen values of time-evolution matrix A which is multiplied to the vector consists of the node temperatures are less than unity. This condition was found as det(A–γE) becomes zero when the argument of complex g in the determinant changed along |γ|=1 around –1 and as the time step is increased. The followings are the results. When the conduction along the flow direction is negligible, the calculation is stable when hA_w, _jΔt/ρc_pV_j≤1.65. When the conduction is significant, no recommended correlation was found for the stability limit. The dimensionless parameter is, however, applicable for various crank angles once the value is determined. The scheme similar to Crank-Nicolson’s was found to be stable for all time step.