add exact solution computation to linear advection

Author: szaghi

src/lib/foodie_integrator_runge_kutta_lssp.f90

@@ -248,7 +248,7 @@ subroutine initialize(self, scheme, U, stages, stop_on_fail)
       allocate(self%alpha(1:self%stages)) ; self%alpha = 0._R_P
       call self%initialize_order_s
     endselect
-    self%description_ = trim(adjustl(scheme))//'_stages_'//trim(str(self%stages))
+    self%description_ = trim(adjustl(scheme))//'_stages_'//trim(str(self%stages, no_sign=.true.))
     self%registers = self%stages
     if (present(U)) call self%allocate_integrand_members(U=U)
   else

src/tests/tester/foodie_test_integrand_ladvection.f90

@@ -152,6 +152,14 @@ pure function exact_solution(self, t, U0) result(exact)
    class(integrand_object),     intent(in), optional :: U0       !< Initial conditions.
    real(R_P), allocatable                            :: exact(:) !< Exact solution.
 
+   if (present(U0)) then
+      select type(U0)
+      type is(integrand_ladvection)
+         exact = U0%u(1:self%Ni)
+      endselect
+   else
+      exact = self%u(1:self%Ni) * 0._R_P
+   endif
    endfunction exact_solution
 
    subroutine export_tecplot(self, file_name, t, scheme, close_file)

src/tests/tester/foodie_tester.f90

@@ -349,6 +349,7 @@ subroutine integrand_compute_error
 
       select type(integrand)
       type is(integrand_ladvection)
+         error = abs(integrand%output() - integrand%exact_solution(t=time))
       type is(integrand_oscillation)
          error = abs(integrand%output() - integrand%exact_solution(t=time))
       endselect