This article presents a method to calculate the average acoustic intensity during ultrasound simulation using a new approach that exploits compression of intermediate results. One of the applications of high-intensity focused ultrasound (HIFU) simulations is the calculation of the thermal dose, which indicates the amount of tissue destroyed using a state-of-the-art k-space pseudospectral method. The thermal simulation is preceded by the calculation of the average intensity within the acoustic simulation. Due to the time staggering between the particle velocity and the acoustic pressure used in such simulations, the average intensity calculation is typically executed offline after the acoustic simulation consuming both disk space and time (the data can spread over terabytes). Our new approach calculates the average intensity during the acoustic simulation using the output coefficients of a new compression method which enables resolving the time staggering on-the-fly with huge disk space savings. To reduce RAM requirements, the article also presents a new 40-bit method for encoding compression complex coefficients. Experimental numerical simulations with the proposed method have shown that disk space requirements are up to 99% lower. The simulation speed was not significantly affected by the approach and the compression error did not affect the prediction accuracy of the thermal dose. From the standpoint of supercomputers, the new approach is significantly more economical. Saving computing resources increases the chances of real use of acoustic simulations in practice. The method can be applied to signals of a similar character, e.g., for electromagnetic radio waves.