[H-DS06] Tsunami and tsunami forecast

[HDS06-13] Detailed CFL Conditions for Numerical Tsunami Calculations
- Investigation of its Calculation Accuracy and Speed

*Masaaki MINAMI¹ (1.Meteorological Research Institute)

Keywords:CFL Condition, Computational Stability Conditions, Real-time Tsunami Prediction

When considering real-time tsunami simulation as an operation for disaster prevention, the stability of the numerical calculation is the most important factor that directly affects the success or failure of the operation. However, calculation speed is equally important in real-time simulations. In most cases, there is a trade-off between "calculation stability" and "calculation speed/precision". In this study, I investigate the CFL condition, which is a basic condition for computational stability, to improve the computational speed and stability of numerical tsunami calculations without compromising accuracy.The CFL condition is a stability condition for calculations presented by Courant, R.; Friedrichs, K.; Lewy, H. (1956) [1928] and is expressed as (1). It is often used as (2) in tsunami calculations (e.g., The Headquarters for Earthquake Research Promotion, Tsunami prediction method for earthquakes with characterized source faults). However, the ocean model of Mellor, G. L. (2004) (hereafter referred to as POM) presents the condition (3). Therefore, in this paper, I calculated a large number of cases by varying the grid spacing Δx, Δy, and the integration time interval Δt in various ways, and found the maximum Δt at which the calculation is stable, thereby obtaining the maximum Courant number that can be calculated stably. The results are shown in Fig. 1, and the conditions are consistent with those of the POM. It was found that these conditions can be obtained by geometrically determining the shortest length of the grid spacing for calculating wave height and the grid spacing for calculating flux. In this paper, the condition (4) is used to apply these conditions to a spherical coordinate system (a coordinate system using latitude and longitude, which is often used in tsunami calculations). Although these conditions need to be checked for each mesh, they need to be calculated only once in advance, and the computational burden is negligible. The maximum Δt is 1.31 sec for the 30 arcsec grid (the range of Fig. 2) for the entire Pacific Ocean. In these calculations, Δt=1.00sec is often used. Therefore, using JAGURS (Baba et al., 2015), I performed calculations for the 2010 Chilean tsunami using Δt=1.31sec in these regions, and found that the calculations were stable and the results were almost the same as for Δt=1.00sec. The calculation time was speeded up by about 24% because the Δt was 1.31 times larger and the number of integrations was 1/1.31 times smaller.