Add two-sided Zalesak-type IDP subcell limiting

NEWS.md

@@ -13,6 +13,7 @@ for human readability.
 - Capability to set truly discontinuous initial conditions in 1D.
 - Wetting and drying feature and examples for 1D and 2D shallow water equations
 - Implementation of the polytropic Euler equations in 2D
+- Implementation of the quasi-1D shallow water equations
 - Subcell (positivity and local min/max) limiting support for conservative variables
   in 2D for `TreeMesh`
 - AMR for hyperbolic-parabolic equations on 2D/3D `TreeMesh`

examples/tree_2d_dgsem/elixir_euler_blast_wave_sc_subcell_nonperiodic.jl

@@ -0,0 +1,93 @@
+
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations2D(1.4)
+
+"""
+    initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D)
+
+A medium blast wave taken from
+- Sebastian Hennemann, Gregor J. Gassner (2020)
+  A provably entropy stable subcell shock capturing approach for high order split form DG
+  [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044)
+"""
+function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D)
+    # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave"
+    # Set up polar coordinates
+    inicenter = SVector(0.0, 0.0)
+    x_norm = x[1] - inicenter[1]
+    y_norm = x[2] - inicenter[2]
+    r = sqrt(x_norm^2 + y_norm^2)
+    phi = atan(y_norm, x_norm)
+    sin_phi, cos_phi = sincos(phi)
+
+    # Calculate primitive variables
+    rho = r > 0.5 ? 1.0 : 1.1691
+    v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi
+    v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi
+    p = r > 0.5 ? 1.0E-3 : 1.245
+
+    return prim2cons(SVector(rho, v1, v2, p), equations)
+end
+initial_condition = initial_condition_blast_wave
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+
+surface_flux = flux_lax_friedrichs
+volume_flux = flux_ranocha
+basis = LobattoLegendreBasis(3)
+limiter_idp = SubcellLimiterIDP(equations, basis;
+                                local_minmax_variables_cons = ["rho"])
+volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
+                                                volume_flux_dg = volume_flux,
+                                                volume_flux_fv = surface_flux)
+solver = DGSEM(basis, surface_flux, volume_integral)
+
+coordinates_min = (-2.0, -2.0)
+coordinates_max = (2.0, 2.0)
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 6,
+                n_cells_max = 10_000,
+                periodicity = false)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    boundary_conditions = boundary_condition)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 2.0)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 100
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+stepsize_callback = StepsizeCallback(cfl = 0.3)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false))
+
+sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks);
+                  dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+                  save_everystep = false, callback = callbacks);
+summary_callback() # print the timer summary

examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl

@@ -14,49 +14,48 @@ The Sedov blast wave setup based on Flash
 - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000
 """
 function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D)
-  # Set up polar coordinates
-  inicenter = SVector(0.0, 0.0)
-  x_norm = x[1] - inicenter[1]
-  y_norm = x[2] - inicenter[2]
-  r = sqrt(x_norm^2 + y_norm^2)
-
-  # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000
-  r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6)
-  # r0 = 0.5 # = more reasonable setup
-  E = 1.0
-  p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2)
-  p0_outer = 1.0e-5 # = true Sedov setup
-  # p0_outer = 1.0e-3 # = more reasonable setup
-
-  # Calculate primitive variables
-  rho = 1.0
-  v1  = 0.0
-  v2  = 0.0
-  p   = r > r0 ? p0_outer : p0_inner
-
-  return prim2cons(SVector(rho, v1, v2, p), equations)
+    # Set up polar coordinates
+    inicenter = SVector(0.0, 0.0)
+    x_norm = x[1] - inicenter[1]
+    y_norm = x[2] - inicenter[2]
+    r = sqrt(x_norm^2 + y_norm^2)
+
+    # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000
+    r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6)
+    # r0 = 0.5 # = more reasonable setup
+    E = 1.0
+    p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2)
+    p0_outer = 1.0e-5 # = true Sedov setup
+    # p0_outer = 1.0e-3 # = more reasonable setup
+
+    # Calculate primitive variables
+    rho = 1.0
+    v1 = 0.0
+    v2 = 0.0
+    p = r > r0 ? p0_outer : p0_inner
+
+    return prim2cons(SVector(rho, v1, v2, p), equations)
 end
 initial_condition = initial_condition_sedov_blast_wave
 
 surface_flux = flux_lax_friedrichs
-volume_flux  = flux_chandrashekar
+volume_flux = flux_chandrashekar
 basis = LobattoLegendreBasis(3)
 limiter_idp = SubcellLimiterIDP(equations, basis;
-                                local_minmax_variables_cons=[1])
+                                local_minmax_variables_cons = ["rho"])
 volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
-                                                volume_flux_dg=volume_flux,
-                                                volume_flux_fv=surface_flux)
+                                                volume_flux_dg = volume_flux,
+                                                volume_flux_fv = surface_flux)
 solver = DGSEM(basis, surface_flux, volume_integral)
 
 coordinates_min = (-2.0, -2.0)
-coordinates_max = ( 2.0,  2.0)
+coordinates_max = (2.0, 2.0)
 mesh = TreeMesh(coordinates_min, coordinates_max,
-                initial_refinement_level=3,
-                n_cells_max=100_000)
+                initial_refinement_level = 3,
+                n_cells_max = 100_000)
 
 semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
 
-
 ###############################################################################
 # ODE solvers, callbacks etc.
 
@@ -66,16 +65,16 @@ ode = semidiscretize(semi, tspan)
 summary_callback = SummaryCallback()
 
 analysis_interval = 1000
-analysis_callback = AnalysisCallback(semi, interval=analysis_interval)
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
 
-alive_callback = AliveCallback(analysis_interval=analysis_interval)
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
 
-save_solution = SaveSolutionCallback(interval=1000,
-                                     save_initial_solution=true,
-                                     save_final_solution=true,
-                                     solution_variables=cons2prim)
+save_solution = SaveSolutionCallback(interval = 1000,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
 
-stepsize_callback = StepsizeCallback(cfl=0.6)
+stepsize_callback = StepsizeCallback(cfl = 0.6)
 
 callbacks = CallbackSet(summary_callback,
                         analysis_callback, alive_callback,
@@ -84,9 +83,9 @@ callbacks = CallbackSet(summary_callback,
 ###############################################################################
 # run the simulation
 
-stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false))
+stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false))
 
-sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks);
-                  dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
-                  save_everystep=false, callback=callbacks);
+sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks);
+                  dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+                  save_everystep = false, callback = callbacks);
 summary_callback() # print the timer summary

examples/tree_2d_dgsem/elixir_euler_shockcapturing_subcell.jl

@@ -39,7 +39,7 @@ surface_flux = flux_lax_friedrichs
 volume_flux = flux_ranocha
 basis = LobattoLegendreBasis(3)
 limiter_idp = SubcellLimiterIDP(equations, basis;
-                                positivity_variables_cons = [1],
+                                positivity_variables_cons = ["rho"],
                                 positivity_correction_factor = 0.5)
 volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
                                                 volume_flux_dg = volume_flux,