diff --git a/src/equations/polytropic_euler_2d.jl b/src/equations/polytropic_euler_2d.jl
index f5d2f7b0bad..b3b888ba95d 100644
--- a/src/equations/polytropic_euler_2d.jl
+++ b/src/equations/polytropic_euler_2d.jl
@@ -301,6 +301,46 @@ end
     return abs(v1) + c, abs(v2) + c
 end
 
+# Calculate maximum wave speed for local Lax-Friedrichs-type dissipation as the
+# maximum velocity magnitude plus the maximum speed of sound
+@inline function max_abs_speed_naive(u_ll, u_rr, orientation::Integer,
+                                     equations::PolytropicEulerEquations2D)
+    rho_ll, v1_ll, v2_ll = cons2prim(u_ll, equations)
+    rho_rr, v1_rr, v2_rr = cons2prim(u_rr, equations)
+
+    # Get the velocity value in the appropriate direction
+    if orientation == 1
+        v_ll = v1_ll
+        v_rr = v1_rr
+    else # orientation == 2
+        v_ll = v2_ll
+        v_rr = v2_rr
+    end
+    # Calculate sound speeds (we have p = kappa * rho^gamma)
+    c_ll = sqrt(equations.gamma * equations.kappa * rho_ll^(equations.gamma - 1))
+    c_rr = sqrt(equations.gamma * equations.kappa * rho_rr^(equations.gamma - 1))
+
+    λ_max = max(abs(v_ll), abs(v_rr)) + max(c_ll, c_rr)
+end
+
+@inline function max_abs_speed_naive(u_ll, u_rr, normal_direction::AbstractVector,
+                                     equations::PolytropicEulerEquations2D)
+    rho_ll, v1_ll, v2_ll = cons2prim(u_ll, equations)
+    rho_rr, v1_rr, v2_rr = cons2prim(u_rr, equations)
+
+    # Calculate normal velocities and sound speed (we have p = kappa * rho^gamma)
+    # left
+    v_ll = v1_ll * normal_direction[1] +
+           v2_ll * normal_direction[2]
+    c_ll = sqrt(equations.gamma * equations.kappa * rho_ll^(equations.gamma - 1))
+    # right
+    v_rr = v1_rr * normal_direction[1] + 
+           v2_rr * normal_direction[2]
+    c_rr = sqrt(equations.gamma * equations.kappa * rho_rr^(equations.gamma - 1))
+
+    return max(abs(v_ll), abs(v_rr)) + max(c_ll, c_rr) * norm(normal_direction)
+end
+
 # Convert conservative variables to primitive
 @inline function cons2prim(u, equations::PolytropicEulerEquations2D)
     rho, rho_v1, rho_v2 = u