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| # Isentropic vortex problem (2D) | ||
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| Reference: Coralic, V., & Colonius, T. (2014). Finite-volume Weno scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274, 95–121. https://doi.org/10.1016/j.jcp.2014.06.003 | ||
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| ## Density | ||
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|  | ||
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| ## Density Norms | ||
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|  |
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| import math | ||
| import json | ||
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| # Parameters | ||
| epsilon = '5d0' | ||
| alpha = '1d0' | ||
| gamma = '1.4' | ||
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| # Initial conditions | ||
| vel1_i = '0d0' | ||
| vel2_i = '0d0' | ||
| T_i = '1d0' | ||
| alpha_rho1_i = '1d0' | ||
| pres_i = '1d0' | ||
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| # Perturbations | ||
| vel1 = f'{vel1_i} + (y - yc)*({epsilon}/(2d0*pi))*' + \ | ||
| f'exp({alpha}*(1d0 - (x - xc)**2d0 - (y - yc)**2d0))' | ||
| vel2 = f'{vel2_i} - (x - xc)*({epsilon}/(2d0*pi))*' + \ | ||
| f'exp({alpha}*(1d0 - (x - xc)**2d0 - (y - yc)**2d0))' | ||
| alpha_rho1 = f'{alpha_rho1_i}*(1d0 - ({alpha_rho1_i}/{pres_i})*({epsilon}/(2d0*pi))*' + \ | ||
| f'({epsilon}/(8d0*{alpha}*({gamma} + 1d0)*pi))*' + \ | ||
| f'exp(2d0*{alpha}*(1d0 - (x - xc)**2d0' + \ | ||
| f'- (y - yc)**2d0))' + \ | ||
| f')**{gamma}' | ||
| pres = f'{pres_i}*(1d0 - ({alpha_rho1_i}/{pres_i})*({epsilon}/(2d0*pi))*' + \ | ||
| f'({epsilon}/(8d0*{alpha}*({gamma} + 1d0)*pi))*' + \ | ||
| f'exp(2d0*{alpha}*(1d0 - (x - xc)**2d0' + \ | ||
| f'- (y - yc)**2d0))' + \ | ||
| f')**({gamma} + 1d0)' | ||
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| # Numerical setup | ||
| Nx = 399 | ||
| dx = 10./(1.*(Nx+1)) | ||
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| c = 1.4**0.5 | ||
| C = 0.3 | ||
| mydt = C * dx / c * 0.01 | ||
| Nt = 1/mydt | ||
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| # Configuring case dictionary | ||
| print(json.dumps({ | ||
| # Logistics ================================================================ | ||
| 'run_time_info' : 'T', | ||
| # ========================================================================== | ||
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| # Computational Domain Parameters ========================================== | ||
| 'x_domain%beg' : -3, | ||
| 'x_domain%end' : 3, | ||
| 'y_domain%beg' : -3, | ||
| 'y_domain%end' : 3, | ||
| 'stretch_x' : True, | ||
| 'stretch_y' : True, | ||
| 'loops_x' : 2, | ||
| 'loops_y' : 2, | ||
| 'a_x' : 1.03, | ||
| 'a_y' : 1.03, | ||
| 'x_a' : -1.5, | ||
| 'y_a' : -1.5, | ||
| 'x_b' : 1.5, | ||
| 'y_b' : 1.5, | ||
| 'm' : Nx, | ||
| 'n' : Nx, | ||
| 'p' : 0, | ||
| 'dt' : mydt, | ||
| 't_step_start' : 0, | ||
| 't_step_stop' : 10, | ||
| 't_step_save' : 1, | ||
| # ========================================================================== | ||
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| # Simulation Algorithm Parameters ========================================== | ||
| 'num_patches' : 1, | ||
| 'model_eqns' : 3, | ||
| 'alt_soundspeed' : 'F', | ||
| 'num_fluids' : 1, | ||
| 'adv_alphan' : 'T', | ||
| 'mpp_lim' : 'F', | ||
| 'mixture_err' : 'F', | ||
| 'time_stepper' : 3, | ||
| 'weno_order' : 5, | ||
| 'weno_eps' : 1.E-16, | ||
| 'mapped_weno' : 'T', | ||
| 'null_weights' : 'F', | ||
| 'mp_weno' : 'F', | ||
| 'riemann_solver' : 2, | ||
| 'wave_speeds' : 1, | ||
| 'avg_state' : 2, | ||
| 'bc_x%beg' : -4, | ||
| 'bc_x%end' : -4, | ||
| 'bc_y%beg' : -4, | ||
| 'bc_y%end' : -4, | ||
| # ========================================================================== | ||
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| # Formatted Database Files Structure Parameters ============================ | ||
| 'format' : 1, | ||
| 'precision' : 2, | ||
| 'prim_vars_wrt' :'T', | ||
| 'parallel_io' :'F', | ||
| 'omega_wrt(3)' :'T', | ||
| 'fd_order' : 2, | ||
| # ========================================================================== | ||
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| # Patch 1 ================================================================== | ||
| 'patch_icpp(1)%geometry' : 3, | ||
| 'patch_icpp(1)%x_centroid' : 0, | ||
| 'patch_icpp(1)%y_centroid' : 0, | ||
| 'patch_icpp(1)%length_x' : 10., | ||
| 'patch_icpp(1)%length_y' : 10., | ||
| 'patch_icpp(1)%vel(1)' : vel1, | ||
| 'patch_icpp(1)%vel(2)' : vel2, | ||
| 'patch_icpp(1)%pres' : pres, | ||
| 'patch_icpp(1)%alpha_rho(1)' : alpha_rho1, | ||
| 'patch_icpp(1)%alpha(1)' : 1., | ||
| # ========================================================================== | ||
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| # Fluids Physical Parameters =============================================== | ||
| 'fluid_pp(1)%gamma' : 1.E+00/(1.4-1.E+00), | ||
| 'fluid_pp(1)%pi_inf' : 0.0, | ||
| # ========================================================================== | ||
| })) | ||
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| # ============================================================================== |
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