Development of a Numerical Method for Analyzing Fire Plume Equations Using an Improved Version of a Quasi-Third-Order Accurate CIP Method That Eliminates Numerical Oscillation

Abstract

This study is concerned with simulations of fire phenomena using field equation models. When performing numerical computation of a fire plume accompanied by gas and smoke, the phenomena are expressed through simultaneous non-stationary nonlinear second-order partial differential equations containing advective terms. Those advective terms are then subjected to difference approximations. The ordinary CIP method, which allows us to find an approximate solution using a third-order interpolation function, is often influenced by numerical oscillations emerging specifically with the third-order accuracy, thereby drastically reducing the numerical stability. We developed a new computational algorithm called mCIP method to eliminate these numerical oscillations generated in the numerical computation of partial differential equations when a third-order accurate method is used. A characteristic feature of this mCIP is that it is based on the first-order upwind difference scheme, which does not generate numerical oscillations in those regions where such oscillations may normally occur. We successfully evaluated the performance of this mCIP method and verified its effectiveness by comparing the results of computations with other representative methods, such as CIP method, TVD method and first-order accurate difference method.