-<matplotlib.image.AxesImage at 0x7f45c43efc10>
+<matplotlib.image.AxesImage at 0x7f42a8547e90>
-<matplotlib.colorbar.Colorbar at 0x7fa7af52c890>
+<matplotlib.colorbar.Colorbar at 0x7f86eafd9190>
-<matplotlib.colorbar.Colorbar at 0x7fa7af682ed0>
+<matplotlib.colorbar.Colorbar at 0x7f86ed12cd10>
where \(\rho_\mathrm{begin}\) is the density where the sponge turns on
-(set by sponge.sponge_rho_begin) and rho_mathrm{full}$ is the
+(set by sponge.sponge_rho_begin) and \(\rho_\mathrm{full}\) is the
density where the sponge is fully enabled (set by
sponge.sponge_rho_begin), with \(\rho_\mathrm{begin} >
\rho_\mathrm{full}\).
-<matplotlib.image.AxesImage at 0x7fcf180d03d0>
+<matplotlib.image.AxesImage at 0x7fe3589c8c90>
-<matplotlib.image.AxesImage at 0x7fcf0ed03510>
+<matplotlib.image.AxesImage at 0x7fe358267c90>
-<matplotlib.colorbar.Colorbar at 0x7f26a80e0590>
+<matplotlib.colorbar.Colorbar at 0x7fcec032c8d0>
-<matplotlib.colorbar.Colorbar at 0x7f269d11e3d0>
+<matplotlib.colorbar.Colorbar at 0x7fcec01eca10>
advection_fv4 Solver", "Advection", "Analysis routines", "Burgers\u2019 Equation", "Convergence of the compressible solvers", "Comparing the Compressible Solvers", "Compressible hydrodynamics", "Compressible exercises", "Compressible example problems", "Compressible source terms", "Design ideas", "Diffusion", "Contributing and getting help", "Incompressible hydrodynamics", "pyro: a python hydro code", "Setting up pyro", "Introduction to pyro", "Low Mach number hydrodynamics", "Mesh examples", "Mesh overview", "pyro", "Multigrid Solvers", "Constant-Coefficient Poisson Equation", "General Linear Elliptic Equation", "Variable Coefficient Poisson", "Simple Multigrid Examples", "Notes on the numerical methods", "Working with output", "Particles", "Adding a problem", "pyro package", "pyro.advection package", "pyro.advection.problems package", "pyro.advection_fv4 package", "pyro.advection_fv4.problems package", "pyro.advection_nonuniform package", "pyro.advection_nonuniform.problems package", "pyro.advection_rk package", "pyro.advection_rk.problems package", "pyro.advection_weno package", "pyro.advection_weno.problems package", "pyro.burgers package", "pyro.burgers.problems package", "pyro.burgers_viscous package", "pyro.burgers_viscous.problems package", "pyro.compressible package", "pyro.compressible.problems package", "pyro.compressible_fv4 package", "pyro.compressible_fv4.problems package", "pyro.compressible_react package", "pyro.compressible_react.problems package", "pyro.compressible_rk package", "pyro.compressible_rk.problems package", "pyro.compressible_sdc package", "pyro.compressible_sdc.problems package", "pyro.diffusion package", "pyro.diffusion.problems package", "pyro.incompressible package", "pyro.incompressible.problems package", "pyro.incompressible_viscous package", "pyro.incompressible_viscous.problems package", "pyro.lm_atm package", "pyro.lm_atm.problems package", "pyro.mesh package", "pyro.multigrid package", "pyro.multigrid.examples package", "pyro.particles package", "pyro.swe package", "pyro.swe.problems package", "pyro.util package", "Horizontal Averages of Rayleigh-Taylor", "Running", "Spherical Polar Grid", "Shallow water hydrodynamics", "Testing", "References"], "titleterms": {"about": 16, "acknowledg": 0, "acoustic_puls": [8, 48, 50, 54, 56, 70, 75], "ad": 31, "advect": [3, 8, 33, 34, 48, 50, 54, 56, 70, 75], "advection_fv4": [2, 3, 35, 36], "advection_nonuniform": [3, 37, 38], "advection_rk": [3, 39, 40], "advection_weno": [3, 41, 42], "advective_flux": [33, 37], "analysi": 4, "array_index": 65, "arrayindex": 20, "averag": 72, "bc": [47, 61], "boundari": 65, "bubbl": [8, 10, 19, 48, 50, 54, 56, 64], "burger": [5, 43, 44], "burgers_interfac": 43, "burgers_visc": [45, 46], "caviti": [15, 62], "check": 25, "class": 73, "coarsen": 20, "code": 16, "coeffici": [24, 26], "commandlin": 73, "compar": [7, 26, 71], "comparison": 7, "compress": [6, 7, 8, 9, 10, 11, 47, 48], "compressible_fv4": [6, 8, 11, 49, 50], "compressible_react": [51, 52], "compressible_rk": [8, 11, 53, 54], "compressible_sdc": [8, 11, 55, 56], "constant": 24, "contribut": 14, "convect": [8, 48, 50, 54, 56], "converg": [5, 6, 15, 44, 46, 60, 62], "dam": [70, 75], "data": 20, "defin": 1, "depend": 11, "deriv": [47, 69], "design": 12, "differenc": 20, "diffus": [13, 57, 58], "directori": 12, "discuss": 14, "driver": 12, "edge_coeff": 66, "ellipt": 25, "eo": 47, "equat": [5, 24, 25], "error": 2, "exact": 26, "exampl": [3, 5, 10, 13, 15, 20, 27, 67, 75], "exercis": [3, 9, 13, 15, 27, 75], "explor": [3, 9, 13, 15, 27, 75], "extens": [3, 9, 13, 15, 27, 75], "flame": 52, "flux": [35, 39, 41, 49, 53], "fourth_ord": 65, "fv": 65, "gaussian": [13, 58], "gener": [3, 25], "general_mg": 66, "get": 14, "graviti": 11, "gresho": [8, 48, 50, 54, 56], "grid": [20, 74], "heat": [8, 48, 50, 54, 56], "helmholtz": 7, "help": 14, "histori": 0, "horizont": 72, "hse": [8, 48, 50, 54, 56], "hydro": 16, "hydrodynam": [8, 15, 19, 75], "idea": [3, 12], "implement": [11, 21, 30], "incomp_interfac": 59, "incompress": [15, 59, 60], "incompressible_visc": [15, 61, 62], "indic": 16, "integr": 65, "interfac": [33, 45, 47, 69], "introduct": 18, "inviscid": 5, "io_pyro": 71, "issu": 14, "jupyt": 1, "kelvin": 7, "kh": [8, 48, 50, 54, 56, 70, 75], "known": 27, "linear": 25, "lm_atm": [19, 63, 64], "lm_atm_interfac": 63, "logo": [8, 48, 50, 54, 56, 70, 75], "low": 19, "mach": 19, "main": 12, "manual": 29, "measur": 2, "mesh": [20, 21, 65], "method": 28, "mg": 66, "mg_test_general_alphabeta_onli": 67, "mg_test_general_beta_onli": 67, "mg_test_general_const": 67, "mg_test_general_dirichlet": 67, "mg_test_general_inhomogen": 67, "mg_test_simpl": 67, "mg_test_vc_const": 67, "mg_test_vc_dirichlet": 67, "mg_test_vc_period": 67, "mg_vi": 67, "modul": [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71], "msg": 71, "multigrid": [23, 27, 66, 67], "note": 28, "numba": 12, "number": 19, "numer": 28, "option": 73, "our": 1, "output": 29, "overview": 21, "own": 1, "packag": [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71], "particl": [30, 68], "patch": [21, 65], "perform": 24, "plot": [24, 29, 30, 32], "plot_cav": 62, "plot_tool": 71, "plume": [8, 48, 50, 54, 56], "poisson": [24, 26], "polar": 74, "problem": [1, 3, 5, 8, 10, 11, 13, 15, 19, 31, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 70, 75], "profile_pyro": 71, "project": 27, "project_period": 67, "prolong": 20, "prolong_restrict_demo": 67, "pull": 14, "py": 31, "pyro": [12, 16, 17, 18, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73], "pyro_sim": 32, "python": 16, "quad": [8, 10, 48, 50, 54, 56, 70, 75], "quick": 17, "ramp": [8, 48, 50, 54, 56], "rayleigh": [7, 72], "read": 29, "reconstruct": 65, "refer": 77, "regress": 76, "request": 14, "result": 25, "riemann": 47, "routin": 4, "rt": [8, 10, 48, 50, 52, 54, 56], "rt2": [8, 48, 50, 54, 56], "rt_multimod": [8, 48, 50, 54, 56], "run": 73, "runparam": 71, "runtim": 73, "sedov": [8, 10, 48, 50, 54, 56], "set": [17, 24, 25, 26], "setup": 20, "shallow": 75, "shear": [15, 60, 62], "simpl": 27, "simul": [33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 69], "simulation_nul": 32, "slot": [3, 38], "smooth": [3, 34, 36, 40, 42], "sod": [8, 10, 48, 50, 54, 56], "solut": [24, 26, 27], "solv": [24, 25, 26], "solver": [2, 3, 6, 7, 8, 13, 15, 19, 23, 24, 25, 26, 75], "sourc": 11, "spheric": 74, "spong": 11, "structur": 12, "submodul": [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71], "subpackag": [32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 66, 69], "support": [3, 5, 8, 13, 15, 19, 75], "swe": [69, 70, 75], "system": [25, 26], "tabl": 16, "taylor": [7, 72], "term": 11, "test": [3, 5, 8, 13, 17, 21, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 70, 75, 76], "tophat": [3, 5, 34, 36, 40, 42, 44, 46], "unit": 76, "unsplit_flux": [47, 69], "up": [17, 24, 25, 26], "us": [21, 30], "util": [29, 71], "variabl": [20, 26], "variable_coeff_mg": 66, "verifi": 44, "viscou": 5, "visual": 26, "water": 75, "work": [20, 29]}})
\ No newline at end of file
+Search.setIndex({"alltitles": {"About": [[16, "about"]], "Acknowledgments": [[0, null]], "Adding a problem": [[31, null]], "Advection": [[3, null]], "Analysis routines": [[4, null]], "ArrayIndexer": [[20, "ArrayIndexer"]], "Burgers\u2019 Equation": [[5, null]], "Checking the result": [[25, "Checking-the-result"]], "Coarsening and prolonging": [[20, "Coarsening-and-prolonging"]], "Commandline": [[73, "commandline"]], "Comparing the Compressible Solvers": [[7, null]], "Comparing to the exact solution": [[26, "Comparing-to-the-exact-solution"]], "Comparisons": [[7, "Comparisons"]], "Compressible example problems": [[10, null]], "Compressible exercises": [[9, null]], "Compressible hydrodynamics": [[8, null]], "Compressible source terms": [[11, null]], "Constant-Coefficient Poisson Equation": [[24, null]], "Contributing": [[14, "contributing"]], "Contributing and getting help": [[14, null]], "Convergence of the compressible solvers": [[6, null]], "Defining our own problem in Jupyter": [[1, null]], "Design ideas": [[12, null]], "Differencing": [[20, "Differencing"]], "Diffusion": [[13, null]], "Directory structure": [[12, "directory-structure"]], "Discussions": [[14, "discussions"]], "Error Measurement of the advection_fv4 Solver": [[2, null]], "Example": [[5, "example"], [5, "id5"]], "Example problems": [[10, "example-problems"]], "Examples": [[3, "examples"], [13, "examples"], [15, "examples"], [15, "id8"], [75, "examples"]], "Exercises": [[3, "exercises"], [13, "exercises"], [15, "exercises"], [27, "exercises"], [75, "exercises"]], "Explorations": [[3, "explorations"], [9, "explorations"], [13, "explorations"], [15, "explorations"], [27, "explorations"], [75, "explorations"]], "Extensions": [[3, "extensions"], [9, "extensions"], [13, "extensions"], [15, "extensions"], [27, "extensions"], [75, "extensions"]], "General Linear Elliptic Equation": [[25, null]], "General ideas": [[3, "general-ideas"]], "Gravity": [[11, "gravity"]], "History": [[0, "history"]], "Horizontal Averages of Rayleigh-Taylor": [[72, null]], "Implementation": [[11, "implementation"]], "Incompressible hydrodynamics": [[15, null]], "Indices and tables": [[16, "indices-and-tables"]], "Introduction to pyro": [[18, null]], "Inviscid Burgers": [[5, "inviscid-burgers"]], "Issues": [[14, "issues"]], "Kelvin-Helmholtz": [[7, "Kelvin-Helmholtz"]], "Known Solution": [[27, "known-solution"]], "Low Mach number hydrodynamics": [[19, null]], "Main driver": [[12, "main-driver"]], "Mesh examples": [[20, null]], "Mesh overview": [[21, null]], "Multigrid Solvers": [[23, null]], "Notes on the numerical methods": [[28, null]], "Numba": [[12, "numba"]], "Particles": [[30, null]], "Performing the solve": [[24, "Performing-the-solve"]], "Plotting particles": [[30, "plotting-particles"]], "Plotting the solution": [[24, "Plotting-the-solution"]], "Problem-dependent source": [[11, "problem-dependent-source"]], "Projection": [[27, "projection"]], "Pull Requests": [[14, "pull-requests"]], "Pyro class": [[73, "pyro-class"]], "Quick test": [[17, "quick-test"]], "Rayleigh-Taylor": [[7, "Rayleigh-Taylor"]], "Reading and plotting manually": [[29, "reading-and-plotting-manually"]], "References": [[77, null]], "Regression tests": [[76, "regression-tests"]], "Running": [[73, null]], "Runtime options": [[73, "runtime-options"]], "Sedov": [[10, "sedov"]], "Setting up pyro": [[17, null]], "Setting up the solver": [[24, "Setting-up-the-solver"], [25, "Setting-up-the-solver"], [26, "Setting-up-the-solver"]], "Setup a Grid with Variables": [[20, "Setup-a-Grid-with-Variables"]], "Shallow water hydrodynamics": [[75, null]], "Simple Multigrid Examples": [[27, null]], "Sod": [[10, "sod"]], "Solving the system": [[25, "Solving-the-system"], [26, "Solving-the-system"]], "Spherical Polar Grid": [[74, null]], "Sponge": [[11, "sponge"]], "Submodules": [[32, "submodules"], [33, "submodules"], [34, "submodules"], [35, "submodules"], [36, "submodules"], [37, "submodules"], [38, "submodules"], [39, "submodules"], [40, "submodules"], [41, "submodules"], [42, "submodules"], [43, "submodules"], [44, "submodules"], [45, "submodules"], [46, "submodules"], [47, "submodules"], [48, "submodules"], [49, "submodules"], [50, "submodules"], [51, "submodules"], [52, "submodules"], [53, "submodules"], [54, "submodules"], [55, "submodules"], [56, "submodules"], [57, "submodules"], [58, "submodules"], [59, "submodules"], [60, "submodules"], [61, "submodules"], [62, "submodules"], [63, "submodules"], [64, "submodules"], [65, "submodules"], [66, "submodules"], [67, "submodules"], [68, "submodules"], [69, "submodules"], [70, "submodules"], [71, "submodules"]], "Subpackages": [[32, "subpackages"], [33, "subpackages"], [35, "subpackages"], [37, "subpackages"], [39, "subpackages"], [41, "subpackages"], [43, "subpackages"], [45, "subpackages"], [47, "subpackages"], [49, "subpackages"], [51, "subpackages"], [53, "subpackages"], [55, "subpackages"], [57, "subpackages"], [59, "subpackages"], [61, "subpackages"], [63, "subpackages"], [66, "subpackages"], [69, "subpackages"]], "Testing": [[76, null]], "Tests": [[21, "tests"]], "Unit tests": [[76, "unit-tests"]], "Utilities": [[29, "utilities"]], "Variable Coefficient Poisson": [[26, null]], "Viscous Burgers": [[5, "viscous-burgers"]], "Visualizing the solution": [[26, "Visualizing-the-solution"]], "Working with output": [[29, null]], "Working with the data": [[20, "Working-with-the-data"]], "acoustic_pulse": [[8, "acoustic-pulse"], [75, "acoustic-pulse"]], "advect": [[8, "advect"], [75, "advect"]], "advection solver": [[3, "advection-solver"]], "advection_fv4 solver": [[3, "advection-fv4-solver"]], "advection_nonuniform solver": [[3, "advection-nonuniform-solver"]], "advection_rk solver": [[3, "advection-rk-solver"]], "advection_weno solver": [[3, "advection-weno-solver"]], "bubble": [[8, "bubble"], [10, "bubble"], [19, "bubble"]], "cavity": [[15, "cavity"], [15, "id10"]], "compressible": [[6, "compressible"], [11, "compressible"]], "compressible solver": [[8, "compressible-solver"]], "compressible_fv4": [[6, "compressible_fv4"]], "compressible_fv4 solver": [[8, "compressible-fv4-solver"]], "compressible_rk solver": [[8, "compressible-rk-solver"]], "compressible_rk, compressible_fv4, compressible_sdc": [[11, "compressible-rk-compressible-fv4-compressible-sdc"]], "compressible_sdc solver": [[8, "compressible-sdc-solver"]], "convection": [[8, "convection"]], "converge": [[5, "converge"], [5, "id2"], [15, "converge"], [15, "id6"]], "convergence": [[15, "convergence"], [15, "id13"]], "dam": [[75, "dam"], [75, "id1"]], "diffusion solver": [[13, "diffusion-solver"]], "gaussian": [[13, "gaussian"], [13, "id1"]], "gresho": [[8, "gresho"]], "heating": [[8, "heating"]], "hse": [[8, "hse"]], "incompressible solver": [[15, "incompressible-solver"]], "incompressible_viscous solver": [[15, "incompressible-viscous-solver"]], "kh": [[8, "kh"], [75, "kh"]], "lm_atm solver": [[19, "lm-atm-solver"]], "logo": [[8, "logo"], [75, "logo"]], "mesh.patch implementation and use": [[21, "mesh-patch-implementation-and-use"]], "particles.particles implementation and use": [[30, "particles-particles-implementation-and-use"]], "plume": [[8, "plume"]], "pyro": [[22, null]], "pyro package": [[32, null]], "pyro.advection package": [[33, null]], "pyro.advection.advective_fluxes module": [[33, "module-pyro.advection.advective_fluxes"]], "pyro.advection.interface module": [[33, "module-pyro.advection.interface"]], "pyro.advection.problems package": [[34, null]], "pyro.advection.problems.smooth module": [[34, "module-pyro.advection.problems.smooth"]], "pyro.advection.problems.test module": [[34, "module-pyro.advection.problems.test"]], "pyro.advection.problems.tophat module": [[34, "module-pyro.advection.problems.tophat"]], "pyro.advection.simulation module": [[33, "module-pyro.advection.simulation"]], "pyro.advection_fv4 package": [[35, null]], "pyro.advection_fv4.fluxes module": [[35, "module-pyro.advection_fv4.fluxes"]], 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