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Higher-order upwind schemes on unstructured meshesHigher-order finite volume solvers have been developed for the atmospheric transport equation as well as the Navier-Stokes equations. The solver is based on unstructured triangular grids in two dimensions. Different gradient reconstruction techniques have been tested to achieve higher-order accuracy in space and various slope limiters have been implemented to enforce monotonicity. Higher-order accuracy in time is maintained with the help of multi-stage Runge-Kutta explicit time-marching. Solution-adaptive techniques have also been used to demonstrate the computational efficiency associated with the use of unstructured grids.a. Smolarkiewicz's Deformational Flow Top left: Initial tracer field, top right: Initial flow field (streamfunction), bottom left: Tracer field at 1000 iterations, bottom right: Tracer field at 3000 iterations.
For a description of this test case see: Smolarkiewicz, P. K., 1982: The multi-dimensional Crowley advection scheme. Mon. Wea. Rev., 113, 1050-1065. b. Doswell's Frontogenesis Top left: Initial tracer field, top right: Initial flow field (wind speed), bottom left: Numerical solution at time = 4 units, bottom right: Exact solution at time = 4 units.
For a description of this test case see: Doswell, C., 1984: Kinematic Analysis of Frontogenesis Associated with a Nondivergent Vortex. J. Atmos. Sci., 41, 1242-1248. c. LeVeque's Swirling Deformational Flow Top left: Initial tracer field, top right: Initial flow field (wind speed), bottom left: Tracer field at 2300 iterations, bottom right: Tracer field at 4500 iterations.
For a description of this test case see: LeVeque, R. J., 1996: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal., 33, 627-665. d. Convection in Neutral Atmosphere Top left: Initial potential temp (K), top right: potential temp. (K) after 300s, middle left: u-velocity (m/s) after 300s and middle right: v-velocity (m/s) after 300s into the simulation, bottom left: density after 300s and bottom right: Mach number after 300s into the simulation.
Atmospheric Flow Equation Set (Conservation of Energy in terms of rho-theta), Neutral Atmosphere in hydrostatic balance initially, Warm bubble added near the lower boundary - Velocities set to zero initially, Godunov Method with the HLLC Approximate Riemann Solver, 2D Unstructured Triangular Mesh, All boundaries treated as solid wall See the
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