Stability of the diurnal cycles of an atmospheric boundary layer in a partial differential equation with a finite element model

We use the conservation laws of mass, momentum, energy, and moisture equations derived from a finite element model to assess the stability of diurnal cycles of atmospheric boundary layer flow. The results show the most accurate predictions for how temperature, pressure, and wind speed affect mesoscale flow in various domains, with isentropes remaining stable despite the dynamic influence of initial and damped boundary conditions. The degree of turbulence can fluctuate due to weak temperature and wind gradients. In order to determine which isentropes are stable in a particular area of the cold core and cyclonic system in the lower atmosphere, this work employs the numerical weather prediction (NWP) of adaptive discontinuous finite element Galerkin approach to detect temperature, pressure, wind speed, and magnitude of the turbulence oscillation mode. We select starting mesh point is longitude and latitude values (Chennai), wind speed at 2, 4, 6, 8, 10, 12 m level, temperature and relative humidity, then other nodes are treated as every 50 km distance longitude and latitude value, wind speed at 2, 4, 6, 8, 10, 12 m level, temperature and relative humidity as starting node and ending node values (Coimbatore). The computational domain is rectangular, 550 km in the horizontal and 2000 m height. In order to resolve the frontal movement reasonably well, we discretize the domain into 91 × 91 rectangular bi-quadratic elements with an effective horizontal grid spacing of 2 km, spanning a length of 30 km inland from the shore. © 2025 Elsevier Ltd