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High-order compact MacCormack scheme for two-dimensional compressible and non-hydrostatic equations of the atmosphere |
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| Affiliation: | 1. Department of Meteorology, Science and Research Branch, Islamic Azad University, Tehran, Iran;2. Institute of Geophysics, University of Tehran, Iran;1. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Břehová 7, 115 19 - Praha 1, Czech Republic;2. Retired Fellow, Los Alamos National Laboratory, Los Alamos, NM, USA;1. Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, México D.F. 09340, Mexico;2. Comisión Nacional de Seguridad Nuclear y Salvaguardias, Doctor Barragán 779, Col. Narvarte, México D.F. 03020, Mexico;1. Loughborough University, Leicestershire, LE11 3TU, UK;2. Heriot-Watt University, Edinburgh, EH14 4AS, UK;3. European Centre For Medium Range Weather Forecasts, Reading, RG2 9AX, UK |
| Abstract: | This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge–Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method. |
| Keywords: | Compact MacCormack scheme Atmosphere Numerical accuracy Non-hydrostatic Compressible Warm bubble Cold bubble |
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