diff --git a/examples/2D_kelvin_helmholtz/README.md b/examples/2D_kelvin_helmholtz/README.md
new file mode 100644
index 0000000000..4a87afbfce
--- /dev/null
+++ b/examples/2D_kelvin_helmholtz/README.md
@@ -0,0 +1,10 @@
+# Kelvin-Helmholtz Instability (2D)
+
+Reference: See Example 4.8.
+> A.S. Chamarthi, S.H. Frankel, A. Chintagunta, Implicit gradients based novel finite volume scheme for compressible single and multi-component flows, arXiv preprint arXiv:2106.01738 (2021).
+
+### Initial State
+
+
+### Evolved State
+
diff --git a/examples/2D_kelvin_helmholtz/case.py b/examples/2D_kelvin_helmholtz/case.py
new file mode 100644
index 0000000000..e1fb5a3046
--- /dev/null
+++ b/examples/2D_kelvin_helmholtz/case.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+import json
+import math
+
+
+eps = 1e-6
+time_end = 1.0
+time_save = time_end / 100.0
+
+# Configuring case dictionary
+print(
+ json.dumps(
+ {
+ # Logistics
+ "run_time_info": "T",
+ # Computational Domain Parameters
+ "x_domain%beg": 0,
+ "x_domain%end": 1.0,
+ "y_domain%beg": 0,
+ "y_domain%end": 1.0,
+ "m": 512,
+ "n": 512,
+ "p": 0,
+ "cfl_adap_dt": "T",
+ "cfl_target": 0.2,
+ "n_start": 0,
+ "t_stop": time_end,
+ "t_save": time_save,
+ # Simulation Algorithm Parameters
+ "num_patches": 2,
+ "model_eqns": 2,
+ "alt_soundspeed": "F",
+ "num_fluids": 2,
+ "mpp_lim": "T",
+ "mixture_err": "T",
+ "time_stepper": 3,
+ "weno_order": 5,
+ "weno_eps": 1.0e-10,
+ "null_weights": "F",
+ "mp_weno": "F",
+ "riemann_solver": 1,
+ "wave_speeds": 1,
+ "avg_state": 2,
+ "bc_x%beg": -1,
+ "bc_x%end": -1,
+ "bc_y%beg": -1,
+ "bc_y%end": -1,
+ # Formatted Database Files Structure Parameters
+ "format": 1,
+ "precision": 2,
+ "prim_vars_wrt": "T",
+ "parallel_io": "T",
+ # Background
+ "patch_icpp(1)%geometry": 3,
+ "patch_icpp(1)%hcid": 207,
+ "patch_icpp(1)%x_centroid": 0.5,
+ "patch_icpp(1)%y_centroid": 0.5,
+ "patch_icpp(1)%length_x": 1.0,
+ "patch_icpp(1)%length_y": 1.0,
+ "patch_icpp(1)%vel(1)": -0.5,
+ "patch_icpp(1)%vel(2)": 0.0,
+ "patch_icpp(1)%pres": 2.5,
+ "patch_icpp(1)%alpha_rho(1)": 1.0 - eps,
+ "patch_icpp(1)%alpha(1)": 1.0 - eps,
+ "patch_icpp(1)%alpha_rho(2)": eps,
+ "patch_icpp(1)%alpha(2)": eps,
+ # Center Strip (0.25 < y <= 0.75)
+ "patch_icpp(2)%geometry": 3,
+ "patch_icpp(2)%alter_patch(1)": "T",
+ "patch_icpp(2)%hcid": 207,
+ "patch_icpp(2)%x_centroid": 0.5,
+ "patch_icpp(2)%y_centroid": 0.5,
+ "patch_icpp(2)%length_x": 1.0,
+ "patch_icpp(2)%length_y": 0.5,
+ "patch_icpp(2)%vel(1)": 0.5,
+ "patch_icpp(2)%vel(2)": 0.0,
+ "patch_icpp(2)%pres": 2.5,
+ "patch_icpp(2)%alpha_rho(1)": 2.0 * eps,
+ "patch_icpp(2)%alpha(1)": eps,
+ "patch_icpp(2)%alpha_rho(2)": 2.0 * (1.0 - eps),
+ "patch_icpp(2)%alpha(2)": 1.0 - eps,
+ # Fluids Physical Parameters
+ "fluid_pp(1)%gamma": 1.0e00 / (5.0 / 3.0 - 1.0e00),
+ "fluid_pp(1)%pi_inf": 0.0e00,
+ "fluid_pp(2)%gamma": 1.0e00 / (5.0 / 3.0 - 1.0e00),
+ "fluid_pp(2)%pi_inf": 0.0e00,
+ }
+ )
+)
diff --git a/examples/2D_kelvin_helmholtz/figure0.png b/examples/2D_kelvin_helmholtz/figure0.png
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diff --git a/examples/2D_kelvin_helmholtz/figure1.png b/examples/2D_kelvin_helmholtz/figure1.png
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index 0000000000..f7415bfdbb
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diff --git a/examples/2D_richtmyer_meshkov/README.md b/examples/2D_richtmyer_meshkov/README.md
new file mode 100644
index 0000000000..30ee0ae1b2
--- /dev/null
+++ b/examples/2D_richtmyer_meshkov/README.md
@@ -0,0 +1,10 @@
+# Richtmyer-Meshkov Instability (2D)
+
+Reference: See Example 4.18.
+> A.S. Chamarthi, S.H. Frankel, A. Chintagunta, Implicit gradients based novel finite volume scheme for compressible single and multi-component flows, arXiv preprint arXiv:2106.01738 (2021).
+
+### Initial State
+
+
+### Evolved State
+
diff --git a/examples/2D_richtmyer_meshkov/case.py b/examples/2D_richtmyer_meshkov/case.py
new file mode 100644
index 0000000000..b7dd42553c
--- /dev/null
+++ b/examples/2D_richtmyer_meshkov/case.py
@@ -0,0 +1,97 @@
+#!/usr/bin/env python3
+import json
+import math
+
+
+mu = 1.0e-4
+lambd = 1.0
+time_end = 15.0
+time_save = time_end / 20.0
+eps = 1.0e-6
+
+# Configuring case dictionary
+print(
+ json.dumps(
+ {
+ # Logistics
+ "run_time_info": "T",
+ # Computational Domain Parameters
+ "x_domain%beg": 0,
+ "x_domain%end": 16.0 * lambd,
+ "y_domain%beg": 0,
+ "y_domain%end": lambd,
+ "m": 4096,
+ "n": 256,
+ "p": 0,
+ "cfl_adap_dt": "T",
+ "cfl_target": 0.1,
+ "n_start": 0,
+ "t_stop": time_end,
+ "t_save": time_save,
+ # Simulation Algorithm Parameters
+ "num_patches": 2,
+ "model_eqns": 2,
+ "alt_soundspeed": "F",
+ "num_fluids": 2,
+ "mpp_lim": "T",
+ "mixture_err": "T",
+ "recon_type": 1,
+ "time_stepper": 3,
+ "weno_order": 5,
+ "weno_eps": 1.0e-9,
+ "null_weights": "F",
+ "mapped_weno": "T",
+ "mp_weno": "T",
+ "riemann_solver": 2,
+ "wave_speeds": 1,
+ "avg_state": 2,
+ "bc_x%beg": -17,
+ "bc_x%end": -17,
+ "bc_y%beg": -15,
+ "bc_y%end": -15,
+ # Formatted Database Files Structure Parameters
+ "format": 1,
+ "precision": 2,
+ "prim_vars_wrt": "T",
+ "parallel_io": "T",
+ # Fluid #1 = Heavier Fluid
+ # Fluid #2 = Lighter Fluid
+ # Pre Shock
+ "patch_icpp(1)%geometry": 3,
+ "patch_icpp(1)%hcid": 208,
+ "patch_icpp(1)%x_centroid": 0.5 * 0.7 * lambd,
+ "patch_icpp(1)%y_centroid": 0.5 * lambd,
+ "patch_icpp(1)%length_x": 0.7 * lambd,
+ "patch_icpp(1)%length_y": lambd,
+ "patch_icpp(1)%vel(1)": 1.24,
+ "patch_icpp(1)%vel(2)": 0.0,
+ "patch_icpp(1)%pres": 1.0 / 1.4,
+ "patch_icpp(1)%alpha_rho(1)": 1.0 * eps,
+ "patch_icpp(1)%alpha(1)": eps,
+ "patch_icpp(1)%alpha_rho(2)": 1.0 * (1.0 - eps),
+ "patch_icpp(1)%alpha(2)": (1.0 - eps),
+ # Post Shock
+ "patch_icpp(2)%geometry": 3,
+ "patch_icpp(2)%hcid": 208,
+ "patch_icpp(2)%x_centroid": 0.7 * lambd + 0.5 * 15.3 * lambd,
+ "patch_icpp(2)%y_centroid": 0.5 * lambd,
+ "patch_icpp(2)%length_x": 15.3 * lambd,
+ "patch_icpp(2)%length_y": lambd,
+ "patch_icpp(2)%vel(1)": 0.8787,
+ "patch_icpp(2)%vel(2)": 0.0,
+ "patch_icpp(2)%pres": 1.6272 / 1.4,
+ "patch_icpp(2)%alpha_rho(1)": 1.4112 * eps,
+ "patch_icpp(2)%alpha(1)": eps,
+ "patch_icpp(2)%alpha_rho(2)": 1.4112 * (1.0 - eps),
+ "patch_icpp(2)%alpha(2)": (1.0 - eps),
+ # Fluids Physical Parameters
+ "fluid_pp(1)%gamma": 1.0e00 / (1.093 - 1.0e00),
+ "fluid_pp(1)%pi_inf": 0.0e00,
+ "fluid_pp(2)%gamma": 1.0e00 / (1.4 - 1.0e00),
+ "fluid_pp(2)%pi_inf": 0.0e00,
+ "viscous": "T",
+ "fluid_pp(1)%Re(1)": 1 / mu,
+ "fluid_pp(2)%Re(1)": 1 / mu,
+ }
+ )
+)
diff --git a/examples/2D_richtmyer_meshkov/figure0.png b/examples/2D_richtmyer_meshkov/figure0.png
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diff --git a/examples/2D_richtmyer_meshkov/figure1.png b/examples/2D_richtmyer_meshkov/figure1.png
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index 0000000000..ed0df0beb1
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diff --git a/examples/2D_viscous_shock_tube/README.md b/examples/2D_viscous_shock_tube/README.md
new file mode 100644
index 0000000000..d89015c47e
--- /dev/null
+++ b/examples/2D_viscous_shock_tube/README.md
@@ -0,0 +1,10 @@
+# Viscous Shock Tube (2D)
+
+Reference: See Example 4.13.
+> A.S. Chamarthi, S.H. Frankel, A. Chintagunta, Implicit gradients based novel finite volume scheme for compressible single and multi-component flows, arXiv preprint arXiv:2106.01738 (2021)., see Example 4.13
+
+### Initial State
+
+
+### Evolved State
+
diff --git a/examples/2D_viscous_shock_tube/case.py b/examples/2D_viscous_shock_tube/case.py
new file mode 100644
index 0000000000..fa0dafe86d
--- /dev/null
+++ b/examples/2D_viscous_shock_tube/case.py
@@ -0,0 +1,91 @@
+#!/usr/bin/env python3
+import json
+import math
+
+
+mu = 1.0e-3
+time_end = 1.0
+time_save = time_end / 100.0
+eps = 1.0e-6
+
+# Configuring case dictionary
+print(
+ json.dumps(
+ {
+ # Logistics
+ "run_time_info": "T",
+ # Computational Domain Parameters
+ "x_domain%beg": 0,
+ "x_domain%end": 1.0,
+ "y_domain%beg": 0,
+ "y_domain%end": 0.5,
+ "m": 1280,
+ "n": 640,
+ "p": 0,
+ "cfl_adap_dt": "T",
+ "cfl_target": 0.1,
+ "n_start": 0,
+ "t_stop": time_end,
+ "t_save": time_save,
+ # Simulation Algorithm Parameters
+ "num_patches": 2,
+ "model_eqns": 2,
+ "alt_soundspeed": "F",
+ "num_fluids": 2,
+ "mpp_lim": "T",
+ "mixture_err": "T",
+ "time_stepper": 3,
+ "weno_order": 3,
+ "weno_eps": 1.0e-10,
+ "null_weights": "F",
+ "mapped_weno": "T",
+ "mp_weno": "F",
+ "riemann_solver": 1,
+ "wave_speeds": 1,
+ "avg_state": 1,
+ "bc_x%beg": -8,
+ "bc_x%end": -15,
+ "bc_y%beg": -16,
+ "bc_y%end": -5,
+ # Formatted Database Files Structure Parameters
+ "format": 1,
+ "precision": 2,
+ "prim_vars_wrt": "T",
+ "parallel_io": "T",
+ # Left
+ "patch_icpp(1)%geometry": 3,
+ "patch_icpp(1)%x_centroid": 0.5 * 0.5,
+ "patch_icpp(1)%y_centroid": 0.5 * 0.5,
+ "patch_icpp(1)%length_x": 0.5,
+ "patch_icpp(1)%length_y": 0.5,
+ "patch_icpp(1)%vel(1)": 0.0,
+ "patch_icpp(1)%vel(2)": 0.0,
+ "patch_icpp(1)%pres": 120.0 / (7.0 / 5.0),
+ "patch_icpp(1)%alpha_rho(1)": 120.0 * (1 - eps),
+ "patch_icpp(1)%alpha(1)": 1.0 * (1 - eps),
+ "patch_icpp(1)%alpha_rho(2)": 120.0 * eps,
+ "patch_icpp(1)%alpha(2)": 1.0 * eps,
+ # Right
+ "patch_icpp(2)%geometry": 3,
+ "patch_icpp(2)%x_centroid": 0.5 + 0.5 * 0.5,
+ "patch_icpp(2)%y_centroid": 0.5 * 0.5,
+ "patch_icpp(2)%length_x": 0.5,
+ "patch_icpp(2)%length_y": 0.5,
+ "patch_icpp(2)%vel(1)": 0.0,
+ "patch_icpp(2)%vel(2)": 0.0,
+ "patch_icpp(2)%pres": 1.2 / (7.0 / 5.0),
+ "patch_icpp(2)%alpha_rho(1)": 1.2 * eps,
+ "patch_icpp(2)%alpha(1)": 1.0 * eps,
+ "patch_icpp(2)%alpha_rho(2)": 1.2 * (1 - eps),
+ "patch_icpp(2)%alpha(2)": 1.0 * (1 - eps),
+ # Fluids Physical Parameters
+ "viscous": "T",
+ "fluid_pp(1)%gamma": 1.0e00 / ((7.0 / 5.0) - 1.0e00),
+ "fluid_pp(1)%Re(1)": 1 / mu,
+ "fluid_pp(1)%pi_inf": 0.0,
+ "fluid_pp(2)%gamma": 1.0e00 / ((7.0 / 5.0) - 1.0e00),
+ "fluid_pp(2)%Re(1)": 1 / mu,
+ "fluid_pp(2)%pi_inf": 0.0,
+ }
+ )
+)
diff --git a/examples/2D_viscous_shock_tube/figure0.png b/examples/2D_viscous_shock_tube/figure0.png
new file mode 100644
index 0000000000..b91460651a
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diff --git a/examples/2D_viscous_shock_tube/figure1.png b/examples/2D_viscous_shock_tube/figure1.png
new file mode 100644
index 0000000000..7ca70b6379
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diff --git a/src/common/include/2dHardcodedIC.fpp b/src/common/include/2dHardcodedIC.fpp
index b5de346ea4..ae49fb9952 100644
--- a/src/common/include/2dHardcodedIC.fpp
+++ b/src/common/include/2dHardcodedIC.fpp
@@ -4,6 +4,10 @@
real(wp) :: r, rmax, gam, umax, p0
real(wp) :: rhoH, rhoL, pRef, pInt, h, lam, wl, amp, intH, intL, alph
real(wp) :: factor
+ ! # 207
+ real(wp) :: sigma, gauss1, gauss2
+ ! # 208
+ real(wp) :: ei, d, fsm, alpha_air, alpha_sf6
eps = 1.e-9_wp
#:enddef
@@ -129,6 +133,29 @@
q_prim_vf(advxe)%sf(i, j, 0) = patch_icpp(1)%alpha(2)
end if
+ case (207) ! Kelvin Helmholtz Instability
+ sigma = 0.05_wp/sqrt(2.0_wp)
+ gauss1 = exp(-(y_cc(j) - 0.75_wp)**2/(2.0_wp*sigma**2))
+ gauss2 = exp(-(y_cc(j) - 0.25_wp)**2/(2.0_wp*sigma**2))
+ q_prim_vf(momxb + 1)%sf(i, j, 0) = &
+ 0.1_wp*sin(4.0_wp*pi*x_cc(i))*(gauss1 + gauss2)
+
+ case (208) ! Richtmeyer Meshkov Instability
+ lam = 1.0_wp
+ eps = 1.0e-6_wp
+ ei = 5.0_wp
+ ! Smoothening function to smooth out sharp discontinuity in the interface
+ if (x_cc(i) <