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Abstract The objective of this paper is to develop an optimized implicit‐explicit (IMEX) Runge‐Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX‐SSP2(2,3,2), as it has second‐order accuracy and is composed of diagonally implicit two‐stage and explicit three‐stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit‐Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well‐studied scheme in the same class. In addition, numerical tests confirm that the IMEX‐SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A‐stability property as well as satisfying “second‐stage order” and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.