diff --git a/grudge/models/__init__.py b/grudge/models/__init__.py
index 3fb254b963ac4f3f1401a742ea11d0b5ba98ff18..997207d18be7f02ec29231298cc53c8cfdf7f2db 100644
--- a/grudge/models/__init__.py
+++ b/grudge/models/__init__.py
@@ -39,8 +39,10 @@ class HyperbolicOperator(Operator):
     """A base class for hyperbolic Discontinuous Galerkin operators."""
 
     @abstractmethod
-    def max_eigenvalue(self, t, fields, dcoll):
-        """Return an upperbound on the maximal eigenvalue for the operator."""
+    def max_characteristic_velocity(self, t, fields, dcoll):
+        """Return an upper bound on the characteristic
+        velocities of the operator.
+        """
 
     def estimate_rk4_timestep(self, dcoll, t=None, fields=None, dt_scaling=None):
         """Estimate the largest stable timestep for an RK4 method."""
@@ -48,7 +50,7 @@ class HyperbolicOperator(Operator):
         from grudge.dt_utils import (dt_non_geometric_factor,
                                      dt_geometric_factor)
 
-        max_lambda = self.max_eigenvalue(t, fields, dcoll)
+        max_lambda = self.max_characteristic_velocity(t, fields, dcoll)
         dt_factor = \
             (dt_non_geometric_factor(dcoll, scaling=dt_scaling)
              * dt_geometric_factor(dcoll))
diff --git a/grudge/models/advection.py b/grudge/models/advection.py
index 95baf5545468764dfa7700aca29c841af5ddcc33..2469498aef61fff823d794123992f586cfa1cb39 100644
--- a/grudge/models/advection.py
+++ b/grudge/models/advection.py
@@ -84,7 +84,7 @@ class AdvectionOperatorBase(HyperbolicOperator):
     def weak_flux(self, u_tpair):
         return advection_weak_flux(self.dcoll, self.flux_type, u_tpair, self.v)
 
-    def max_eigenvalue(self, t=None, fields=None, dcoll=None):
+    def max_characteristic_velocity(self, t=None, fields=None, dcoll=None):
         return op.norm(self.dcoll, self.v, 2)
 
 
diff --git a/grudge/models/em.py b/grudge/models/em.py
index f56ca991d3e61485322f2fece95aa805cb27c901..5dcc40933885a55dbcb26ad0b46894c29974b9f5 100644
--- a/grudge/models/em.py
+++ b/grudge/models/em.py
@@ -332,7 +332,7 @@ class MaxwellOperator(HyperbolicOperator):
         """
         return 6*(True,)
 
-    def max_eigenvalue_expr(self):
+    def max_characteristic_vel_expr(self):
         """Return the largest eigenvalue of Maxwell's equations as a hyperbolic
         system.
         """
@@ -344,14 +344,16 @@ class MaxwellOperator(HyperbolicOperator):
             return op.nodal_max(self.dcoll, "vol",
                                 1 / actx.np.sqrt(self.epsilon * self.mu))
 
-    def max_eigenvalue(self, t, fields=None, discr=None, context=None):
+    def max_characteristic_velocity(self, t, fields=None, discr=None, context=None):
         if context is None:
             context = {}
         if self.fixed_material:
-            return self.max_eigenvalue_expr()
+            return self.max_characteristic_vel_expr()
         else:
-            raise ValueError("max_eigenvalue is no longer supported for "
-                    "variable-coefficient problems--use max_eigenvalue_expr")
+            raise ValueError(
+                "max_characteristic_velocity is no longer supported for "
+                "variable-coefficient problems--use max_characteristic_vel_expr"
+            )
 
     def check_bc_coverage(self, mesh):
         from meshmode.mesh import check_bc_coverage
diff --git a/grudge/models/wave.py b/grudge/models/wave.py
index 5001b0b224aee1d72fc479113dd61cbc22463e62..e101fd0443918c3cbb3b5f530a002ff2437578fd 100644
--- a/grudge/models/wave.py
+++ b/grudge/models/wave.py
@@ -175,7 +175,7 @@ class WeakWaveOperator(HyperbolicOperator):
             self.neumann_tag,
             self.radiation_tag])
 
-    def max_eigenvalue(self, t, fields=None, dcoll=None):
+    def max_characteristic_velocity(self, t, fields=None, dcoll=None):
         return abs(self.c)
 
 
@@ -331,7 +331,7 @@ class VariableCoefficientWeakWaveOperator(HyperbolicOperator):
             self.neumann_tag,
             self.radiation_tag])
 
-    def max_eigenvalue(self, t, fields=None, dcoll=None):
+    def max_characteristic_velocity(self, t, fields=None, dcoll=None):
         actx = self.dcoll._setup_actx
         return op.nodal_max(self.dcoll, "vol", actx.np.fabs(self.c))