diff --git a/examples/tree_2d_dgsem/elixir_advection_callbacks.jl b/examples/tree_2d_dgsem/elixir_advection_callbacks.jl
index 51048b4bcee..e38e32dc3c5 100644
--- a/examples/tree_2d_dgsem/elixir_advection_callbacks.jl
+++ b/examples/tree_2d_dgsem/elixir_advection_callbacks.jl
@@ -5,7 +5,14 @@ using Trixi
 module TrixiExtensionExample
 
 using Trixi
-using OrdinaryDiffEqSSPRK: DiscreteCallback, u_modified!
+using OrdinaryDiffEqSSPRK: OrdinaryDiffEqSSPRK, DiscreteCallback
+# To keep backwards compatibility with SciMLBase v2, see
+# https://github.com/trixi-framework/Trixi.jl/pull/2918#issuecomment-4233720339
+@static if isdefined(OrdinaryDiffEqSSPRK, :derivative_discontinuity!)
+    import OrdinaryDiffEqSSPRK: derivative_discontinuity!
+else
+    const derivative_discontinuity! = OrdinaryDiffEqSSPRK.u_modified!
+end
 
 # This is an example implementation for a simple stage callback (i.e., a callable
 # that is executed after each Runge-Kutta *stage*), which records some values
@@ -67,7 +74,7 @@ function (example_callback::ExampleStepCallback)(integrator)
     push!(example_callback.max_values, max_val)
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
diff --git a/src/Trixi.jl b/src/Trixi.jl
index 0d021cb7158..ac57e30845c 100644
--- a/src/Trixi.jl
+++ b/src/Trixi.jl
@@ -41,13 +41,20 @@ using Reexport: @reexport
 using MPI: MPI
 
 @reexport using SciMLBase: CallbackSet
-using SciMLBase: DiscreteCallback,
+using SciMLBase: SciMLBase, DiscreteCallback,
                  ODEProblem, ODESolution,
                  SplitODEProblem
-import SciMLBase: get_du, get_tmp_cache, u_modified!,
+import SciMLBase: get_du, get_tmp_cache,
                   init, step!, check_error,
                   get_proposed_dt, set_proposed_dt!,
                   terminate!, remake, add_tstop!, has_tstop, first_tstop
+# To keep backwards compatibility with SciMLBase v2, see
+# https://github.com/trixi-framework/Trixi.jl/pull/2918#issuecomment-4233720339
+@static if isdefined(SciMLBase, :derivative_discontinuity!)
+    import SciMLBase: derivative_discontinuity!
+else
+    const derivative_discontinuity! = SciMLBase.u_modified!
+end
 
 using DelimitedFiles: readdlm
 using Downloads: Downloads
diff --git a/src/callbacks_step/alive.jl b/src/callbacks_step/alive.jl
index 374a1f68383..b4e63edceb4 100644
--- a/src/callbacks_step/alive.jl
+++ b/src/callbacks_step/alive.jl
@@ -98,7 +98,7 @@ function (alive_callback::AliveCallback)(integrator)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 end # @muladd
diff --git a/src/callbacks_step/amr.jl b/src/callbacks_step/amr.jl
index 0a1995e5dd8..4c0ff99517a 100644
--- a/src/callbacks_step/amr.jl
+++ b/src/callbacks_step/amr.jl
@@ -141,7 +141,7 @@ function initialize!(cb::DiscreteCallback{Condition, Affect!}, u, t,
         iterations = 1
         while has_changed
             compute_coefficients!(integrator.u, t, semi)
-            u_modified!(integrator, true)
+            derivative_discontinuity!(integrator, true)
             has_changed = amr_callback(integrator,
                                        only_refine = amr_callback.adapt_initial_condition_only_refine)
             iterations = iterations + 1
@@ -195,7 +195,7 @@ function (amr_callback::AMRCallback)(integrator; kwargs...)
                                    integrator.t, integrator.iter; kwargs...)
         if has_changed
             resize!(integrator, length(u_ode))
-            u_modified!(integrator, true)
+            derivative_discontinuity!(integrator, true)
         end
     end
 
diff --git a/src/callbacks_step/analysis.jl b/src/callbacks_step/analysis.jl
index 54dd99e9279..4de3f6c2194 100644
--- a/src/callbacks_step/analysis.jl
+++ b/src/callbacks_step/analysis.jl
@@ -358,7 +358,7 @@ function (analysis_callback::AnalysisCallback)(u_ode, du_ode, integrator, semi)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
 
     # Reset performance measurements
     analysis_callback.start_time_last_analysis = time_ns()
diff --git a/src/callbacks_step/averaging.jl b/src/callbacks_step/averaging.jl
index 0bde0f3679e..490c04c226d 100644
--- a/src/callbacks_step/averaging.jl
+++ b/src/callbacks_step/averaging.jl
@@ -79,7 +79,7 @@ function initialize!(cb::DiscreteCallback{Condition, Affect!}, u_ode, t,
                                                         mesh, equations, solver, cache)
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
@@ -111,7 +111,7 @@ function (averaging_callback::AveragingCallback)(integrator)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
 
     return nothing
 end
diff --git a/src/callbacks_step/euler_acoustics_coupling.jl b/src/callbacks_step/euler_acoustics_coupling.jl
index 15b14304962..0fe9dcde175 100644
--- a/src/callbacks_step/euler_acoustics_coupling.jl
+++ b/src/callbacks_step/euler_acoustics_coupling.jl
@@ -211,8 +211,8 @@ function (euler_acoustics_coupling::EulerAcousticsCouplingCallback)(integrator_a
     end
 
     # avoid re-evaluation possible FSAL stages
-    u_modified!(integrator_acoustics, false)
-    u_modified!(integrator_euler, false)
+    derivative_discontinuity!(integrator_acoustics, false)
+    derivative_discontinuity!(integrator_euler, false)
 
     return nothing
 end
diff --git a/src/callbacks_step/glm_speed.jl b/src/callbacks_step/glm_speed.jl
index b094a439ef6..7072734f466 100644
--- a/src/callbacks_step/glm_speed.jl
+++ b/src/callbacks_step/glm_speed.jl
@@ -109,7 +109,7 @@ end
     update_cleaning_speed!(semi, glm_speed_callback, dt, integrator.t)
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
 
     return nothing
 end
diff --git a/src/callbacks_step/save_restart.jl b/src/callbacks_step/save_restart.jl
index 0d6a355dbfe..387316b898d 100644
--- a/src/callbacks_step/save_restart.jl
+++ b/src/callbacks_step/save_restart.jl
@@ -102,7 +102,7 @@ function (restart_callback::SaveRestartCallback)(integrator)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
diff --git a/src/callbacks_step/save_solution.jl b/src/callbacks_step/save_solution.jl
index 62c1973d169..eef76e8c615 100644
--- a/src/callbacks_step/save_solution.jl
+++ b/src/callbacks_step/save_solution.jl
@@ -42,7 +42,7 @@ function get_node_variable(::Val{symbol}, u, mesh, equations, dg, cache,
 end
 ```
 
-For hyperbolic-parabolic equations, `equations_parabolic` and `cache_parabolic` must be 
+For hyperbolic-parabolic equations, `equations_parabolic` and `cache_parabolic` must be
 added:
 ```julia
 function get_node_variable(::Val{symbol}, u, mesh, equations, dg, cache,
@@ -253,7 +253,7 @@ function (solution_callback::SaveSolutionCallback)(integrator)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
diff --git a/src/callbacks_step/stepsize.jl b/src/callbacks_step/stepsize.jl
index a3258a147ef..e32221131c4 100644
--- a/src/callbacks_step/stepsize.jl
+++ b/src/callbacks_step/stepsize.jl
@@ -121,7 +121,7 @@ end
     integrator.dtcache = dt
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
diff --git a/src/callbacks_step/summary.jl b/src/callbacks_step/summary.jl
index 9a06f3ff124..554e779e1ec 100644
--- a/src/callbacks_step/summary.jl
+++ b/src/callbacks_step/summary.jl
@@ -6,7 +6,7 @@
 #! format: noindent
 
 summary_callback(u, t, integrator) = false # when used as condition; never call the summary callback during the simulation
-summary_callback(integrator) = u_modified!(integrator, false) # the summary callback does nothing when called accidentally
+summary_callback(integrator) = derivative_discontinuity!(integrator, false) # the summary callback does nothing when called accidentally
 
 """
     SummaryCallback()
diff --git a/src/callbacks_step/time_series.jl b/src/callbacks_step/time_series.jl
index ff56e32baa6..e3687b7f89a 100644
--- a/src/callbacks_step/time_series.jl
+++ b/src/callbacks_step/time_series.jl
@@ -212,7 +212,7 @@ function (time_series_callback::TimeSeriesCallback)(integrator)
     end
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
 
     return nothing
 end
diff --git a/src/callbacks_step/trivial.jl b/src/callbacks_step/trivial.jl
index 54b00ea384e..dd4fdb6ba8b 100644
--- a/src/callbacks_step/trivial.jl
+++ b/src/callbacks_step/trivial.jl
@@ -17,7 +17,7 @@ function TrivialCallback()
 end
 
 trivial_callback(u, t, integrator) = false
-trivial_callback(integrator) = u_modified!(integrator, false)
+trivial_callback(integrator) = derivative_discontinuity!(integrator, false)
 
 function Base.show(io::IO, cb::DiscreteCallback{<:Any, <:typeof(trivial_callback)})
     @nospecialize cb # reduce precompilation time
diff --git a/src/callbacks_step/visualization.jl b/src/callbacks_step/visualization.jl
index a7d6a31e4e6..bfcc5b31a1d 100644
--- a/src/callbacks_step/visualization.jl
+++ b/src/callbacks_step/visualization.jl
@@ -157,7 +157,7 @@ function (visualization_callback::VisualizationCallback)(integrator)
                  time = integrator.t, timestep = integrator.stats.naccept)
 
     # avoid re-evaluating possible FSAL stages
-    u_modified!(integrator, false)
+    derivative_discontinuity!(integrator, false)
     return nothing
 end
 
diff --git a/src/time_integration/methods_2N.jl b/src/time_integration/methods_2N.jl
index 6bf1314c054..7c693225374 100644
--- a/src/time_integration/methods_2N.jl
+++ b/src/time_integration/methods_2N.jl
@@ -170,7 +170,7 @@ end
 get_tmp_cache(integrator::SimpleIntegrator2N) = (integrator.u_tmp,)
 
 # some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u
-u_modified!(integrator::SimpleIntegrator2N, ::Bool) = false
+derivative_discontinuity!(integrator::SimpleIntegrator2N, ::Bool) = false
 
 # stop the time integration
 function terminate!(integrator::SimpleIntegrator2N)
diff --git a/src/time_integration/methods_3Sstar.jl b/src/time_integration/methods_3Sstar.jl
index e677e33518d..a5e57bddcb5 100644
--- a/src/time_integration/methods_3Sstar.jl
+++ b/src/time_integration/methods_3Sstar.jl
@@ -220,7 +220,7 @@ function get_tmp_cache(integrator::SimpleIntegrator3Sstar)
 end
 
 # some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u
-u_modified!(integrator::SimpleIntegrator3Sstar, ::Bool) = false
+derivative_discontinuity!(integrator::SimpleIntegrator3Sstar, ::Bool) = false
 
 # stop the time integration
 function terminate!(integrator::SimpleIntegrator3Sstar)
diff --git a/src/time_integration/methods_SSP.jl b/src/time_integration/methods_SSP.jl
index e09eddd32d2..a92af77a9f3 100644
--- a/src/time_integration/methods_SSP.jl
+++ b/src/time_integration/methods_SSP.jl
@@ -213,7 +213,7 @@ end
 get_tmp_cache(integrator::SimpleIntegratorSSP) = (integrator.u_tmp,)
 
 # some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u
-u_modified!(integrator::SimpleIntegratorSSP, ::Bool) = false
+derivative_discontinuity!(integrator::SimpleIntegratorSSP, ::Bool) = false
 
 # stop the time integration
 function terminate!(integrator::SimpleIntegratorSSP)
diff --git a/src/time_integration/paired_explicit_runge_kutta/paired_explicit_runge_kutta.jl b/src/time_integration/paired_explicit_runge_kutta/paired_explicit_runge_kutta.jl
index 5de2164fa3e..4dfc44b2089 100644
--- a/src/time_integration/paired_explicit_runge_kutta/paired_explicit_runge_kutta.jl
+++ b/src/time_integration/paired_explicit_runge_kutta/paired_explicit_runge_kutta.jl
@@ -136,7 +136,7 @@ end
 get_tmp_cache(integrator::AbstractPairedExplicitRKIntegrator) = (integrator.u_tmp,)
 
 # some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u
-u_modified!(integrator::AbstractPairedExplicitRKIntegrator, ::Bool) = false
+derivative_discontinuity!(integrator::AbstractPairedExplicitRKIntegrator, ::Bool) = false
 
 # stop the time integration
 function terminate!(integrator::AbstractPairedExplicitRKIntegrator)
diff --git a/src/time_integration/relaxation_methods/relaxation_methods.jl b/src/time_integration/relaxation_methods/relaxation_methods.jl
index b0a793dfae4..a8ccac97039 100644
--- a/src/time_integration/relaxation_methods/relaxation_methods.jl
+++ b/src/time_integration/relaxation_methods/relaxation_methods.jl
@@ -5,7 +5,7 @@ abstract type RelaxationIntegrator <: AbstractTimeIntegrator end
 get_tmp_cache(integrator::RelaxationIntegrator) = (integrator.u_tmp,)
 
 # some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u
-u_modified!(integrator::RelaxationIntegrator, ::Bool) = false
+derivative_discontinuity!(integrator::RelaxationIntegrator, ::Bool) = false
 
 # stop the time integration
 function terminate!(integrator::RelaxationIntegrator)
diff --git a/test/test_aqua.jl b/test/test_aqua.jl
index 154088995ca..8e9aaea1ccf 100644
--- a/test/test_aqua.jl
+++ b/test/test_aqua.jl
@@ -24,6 +24,7 @@ include("test_trixi.jl")
                                                     ignore = (:derivative_operator,
                                                               :periodic_derivative_operator,
                                                               :upwind_operators,
+                                                              :derivative_discontinuity!,
                                                               Symbol("@batch"))))
 end