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Add examples (#573)
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‎examples/3D_TaylorGreenVortex/README.md‎

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# Taylor-Green Vortex (3D)
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Reference: Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD.
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## Final Condition
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This figure shows the isosurface with zero q-criterion.
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![Density](result.png)
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‎examples/3D_TaylorGreenVortex/case.py‎

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#!/usr/bin/env python3
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import math
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import json
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N = 256
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Re = 1600
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L = 1
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P0 = 101325
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rho0 = 1
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C0 = math.sqrt(1.4*P0)
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V0 = 0.1*C0
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mu = V0*L/Re
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cfl = 0.5
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dx = 2*math.pi*L/(N+1)
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dt = cfl * dx / (C0)
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tC = L/V0
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tEnd = 20*tC
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Nt = int(tEnd/dt)
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# Configuring case dictionary
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print(json.dumps({
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# Logistics ================================================
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'run_time_info' : 'T',
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# ==========================================================
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# Computational Domain Parameters ==========================
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'x_domain%beg' : -math.pi*L,
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'x_domain%end' : math.pi*L,
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'y_domain%beg' : -math.pi*L,
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'y_domain%end' : math.pi*L,
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'z_domain%beg' : -math.pi*L,
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'z_domain%end' : math.pi*L,
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'm' : N,
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'n' : N,
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'p' : N,
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'cyl_coord' : 'F',
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'dt' : dt,
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't_step_start' : 13529,
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't_step_stop' : Nt,
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't_step_save' : int(Nt/100),
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# ==========================================================
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# Simulation Algorithm Parameters ==========================
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'num_patches' : 1,
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'model_eqns' : 2,
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'alt_soundspeed' : 'F',
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'num_fluids' : 1,
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'mixture_err' : 'T',
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'time_stepper' : 3,
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'weno_order' : 5,
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'weno_eps' : 1.0E-16,
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'weno_Re_flux' : 'F',
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'weno_avg' : 'F',
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'mapped_weno' : 'T',
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'riemann_solver' : 2,
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'wave_speeds' : 1,
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'avg_state' : 2,
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'bc_x%beg' : -1,
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'bc_x%end' : -1,
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'bc_y%beg' : -1,
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'bc_y%end' : -1,
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'bc_z%beg' : -1,
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'bc_z%end' : -1,
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# ==========================================================
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# Formatted Database Files Structure Parameters ============
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'format' : 1,
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'precision' : 2,
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# 'prim_vars_wrt' :'T',
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'omega_wrt(1)' :'T',
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'omega_wrt(2)' :'T',
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'omega_wrt(3)' :'T',
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'qm_wrt' :'T',
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'fd_order' : 4,
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'parallel_io' :'T',
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# ==========================================================
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# I will use 1 for WATER properties, and 2 for AIR properties
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# Patch 1: Background (AIR - 2) =============================
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'patch_icpp(1)%geometry' : 9,
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'patch_icpp(1)%x_centroid' : 0,
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'patch_icpp(1)%y_centroid' : 0,
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'patch_icpp(1)%z_centroid' : 0,
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'patch_icpp(1)%length_x' : 2*math.pi*L,
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'patch_icpp(1)%length_y' : 2*math.pi*L,
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'patch_icpp(1)%length_z' : 2*math.pi*L,
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'patch_icpp(1)%vel(1)' : f"{V0}*sin(x/{L})*cos(y/{L})*sin(z/{L})",
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'patch_icpp(1)%vel(2)' : f"-{V0}*cos(x/{L})*sin(y/{L})*sin(z/{L})",
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'patch_icpp(1)%vel(3)' : 0,
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'patch_icpp(1)%pres' : f"{P0} + ({rho0}*{V0}**2/16)*(cos(2*x/{L}) + cos(2*y/{L}))*(cos(2*z/{L}) + 2)",
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'patch_icpp(1)%alpha_rho(1)' : 1,
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'patch_icpp(1)%alpha(1)' : 1,
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# ==========================================================
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# Fluids Physical Parameters ===============================
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'fluid_pp(1)%gamma' : 1.0E+00/(1.4-1),
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'fluid_pp(1)%pi_inf' : 0,
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'fluid_pp(1)%Re(1)' : 1/mu,
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# ==========================================================
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}))
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# ==============================================================================

‎examples/3D_TaylorGreenVortex/result.png‎

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‎examples/3D_ibm_bowshock/README.md‎

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# IBM Bow Shock (3D)
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## Final Condition
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![Density](result.png)
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‎examples/3D_ibm/case.py‎ renamed to ‎examples/3D_ibm_bowshock/case.py‎

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‎examples/3D_ibm_bowshock/result.png‎

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‎examples/3D_rayleigh_taylor/README.md‎

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## Centerline Velocities
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![Linear Theory Comparison](linear_theory.jpg)
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![Linear Theory Comparison](linear_theory.png)

‎examples/3D_rayleigh_taylor/linear_theory.jpg‎

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‎examples/3D_rayleigh_taylor/linear_theory.png‎

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