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An Alternative Algorithm for Simulating Flash Flood

Profile image of Muhammad Farizqi KhaldirianMuhammad Farizqi Khaldirian

2021, IOP Conference Series: Earth and Environmental Science

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Abstract

Most of the approaches in numerical modeling techniques are based on the Eulerian coordinate system. This approach faces difficulty in simulating flash flood front propagation. This paper shows an alternative method that implements a numerical modeling technique based on the Lagrangian coordinate system to simulate the water of debris flow. As for the interaction with the riverbed, the simulation uses an Eulerian coordinate system. The method uses the conservative and momentum equations of water and sediment mixture in the Lagrangian form. Source terms represent deposition and erosion. The riverbed in the Eulerian coordinate system interacts with the flow of the mixture. At every step, the algorithm evaluates the relative position of moving nodes of the flow part to the fixed nodes of the riverbed. Computation of advancing velocity and depth uses the riverbed elevation, slope data, and the bed elevation change computation uses the erosion or deposition data of the flow on the moving nodes. Spatial discretization is implementing the Galerkin method. Furthermore, temporal discretization is implementing the forward difference scheme. Test runs show that the algorithm can simulate downward, upward, and reflected backward 1-D flow cases. Two-D model tests and comparisons with SIMLAR software show that the algorithm works in simulating debris flow.

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2.2. Lagrangian Approach na “ In Lagrangian approximation, partial differential equations are derived for moving particles as follows.
2.2. Lagrangian Approach na “ In Lagrangian approximation, partial differential equations are derived for moving particles as follows.
Figure 2. The component of the force acting on the control volume. V is the control volume, A is the area, r is lateral flow parameter and Ss, is the degree of sediment saturation. In the momentum conservation equation, the forces acting on the flow control volume are arranged. In Figure 2 the working momentum is caused by the components of the force, including F'; and F2 which are hydrostatic forces, F3 is gravity and F is the bottom frictional force of the channel. So, the momentum conservation equation can be formulated as follows.
Figure 2. The component of the force acting on the control volume. V is the control volume, A is the area, r is lateral flow parameter and Ss, is the degree of sediment saturation. In the momentum conservation equation, the forces acting on the flow control volume are arranged. In Figure 2 the working momentum is caused by the components of the force, including F'; and F2 which are hydrostatic forces, F3 is gravity and F is the bottom frictional force of the channel. So, the momentum conservation equation can be formulated as follows.
IE I I lf I EE EE The initial conditions are determined by setting a certain depth value at each point of the debris deposit. The initial condition of the debris deposit is at rest. The velocity of the debris particle for the next time step is obtained due to the momentum component of the flow. The boundary condition applies moving boundary following the displacement of the nearest neighbor point in the internal domain area. The depth remains zero at the boundary points. There is no hydrostatic force applied to the outer vertices.
IE I I lf I EE EE The initial conditions are determined by setting a certain depth value at each point of the debris deposit. The initial condition of the debris deposit is at rest. The velocity of the debris particle for the next time step is obtained due to the momentum component of the flow. The boundary condition applies moving boundary following the displacement of the nearest neighbor point in the internal domain area. The depth remains zero at the boundary points. There is no hydrostatic force applied to the outer vertices.
Figure 4. Comparison of modeling results with the analytic solutions of slipping liquid volume travel distances Simulations were carried out with a uniform slope value (tan 6, = 0.3) and several variations of the Manning bed roughness coefficient values of ny = 0.0, ny = 0.03, and ny = 0.06. The centroid traveled distances of the results of each simulation are then compared with the analytic solutions. The results of the modeling give close values to the analytic solution as shown in the following eraph. 3. Results and Discussion
Figure 4. Comparison of modeling results with the analytic solutions of slipping liquid volume travel distances Simulations were carried out with a uniform slope value (tan 6, = 0.3) and several variations of the Manning bed roughness coefficient values of ny = 0.0, ny = 0.03, and ny = 0.06. The centroid traveled distances of the results of each simulation are then compared with the analytic solutions. The results of the modeling give close values to the analytic solution as shown in the following eraph. 3. Results and Discussion
Figure 5. Lagrangian Debris Flow 1-D model test run of flows on a flat anda parabolic beds. Table 1. Test run scenarios.
Figure 5. Lagrangian Debris Flow 1-D model test run of flows on a flat anda parabolic beds. Table 1. Test run scenarios.
The longitudinal bed slope of the channel is constant along the channel from upstream to downstream ends, while the slope of the left and right bank forms a V-shaped channel. In all scenarios, the debris volume discretization points are spaced 1 m from each other before the movement begins. Figure 6 shows that the volume of debris flows upstream to downstream and spreads to the left and right sides due to the absence of a bank slope. The elements stretch with a fixed volume, and the flow depth decreases and the area is expanded.
The longitudinal bed slope of the channel is constant along the channel from upstream to downstream ends, while the slope of the left and right bank forms a V-shaped channel. In all scenarios, the debris volume discretization points are spaced 1 m from each other before the movement begins. Figure 6 shows that the volume of debris flows upstream to downstream and spreads to the left and right sides due to the absence of a bank slope. The elements stretch with a fixed volume, and the flow depth decreases and the area is expanded.
_— — — Figure 7 and Figure 8 show the maximum depth at the initial conditions is set to 1 m. The maximum distance between the upstream and downstream boundaries is 9.0 m. The maximum distance between the left and right boundaries is 4.0 m. Meanwhile, after a 5 s run, the maximum depth is 0.173 m. The maximum distance between the upstream and downstream boundaries is 17.11 m. The maximum distance between the left and right boundaries is 12.09 m. The front of debris travels 16.22 m in 5 seconds.
_— — — Figure 7 and Figure 8 show the maximum depth at the initial conditions is set to 1 m. The maximum distance between the upstream and downstream boundaries is 9.0 m. The maximum distance between the left and right boundaries is 4.0 m. Meanwhile, after a 5 s run, the maximum depth is 0.173 m. The maximum distance between the upstream and downstream boundaries is 17.11 m. The maximum distance between the left and right boundaries is 12.09 m. The front of debris travels 16.22 m in 5 seconds.
Figure 10. Cross-section for Lagrangian run test O1S1. In the scenario as shown in Figure 9, the element's tendency to expand also occurs dominated by widening towards the left and right side of the channel. The velocity at the upstream boundary is smaller than the downstream velocity due to the difference in hydrostatic resistance in the direction of propagation.
Figure 10. Cross-section for Lagrangian run test O1S1. In the scenario as shown in Figure 9, the element's tendency to expand also occurs dominated by widening towards the left and right side of the channel. The velocity at the upstream boundary is smaller than the downstream velocity due to the difference in hydrostatic resistance in the direction of propagation.
Figure 11. Long-section for Lagrangian model run test 01S1.
Figure 11. Long-section for Lagrangian model run test 01S1.
Modeling test using SIMLAR program is carried out for the same scenario to compare the results of modeling debris flow behavior with different approaches. In modeling using SIMLAR program, the elements do not move, the discretization points remain at a certain position (Eulerian coordinate system), so the solution provides parameter changes at the discretization points over time.
Modeling test using SIMLAR program is carried out for the same scenario to compare the results of modeling debris flow behavior with different approaches. In modeling using SIMLAR program, the elements do not move, the discretization points remain at a certain position (Eulerian coordinate system), so the solution provides parameter changes at the discretization points over time.
SIMLAR test for bed slope of 1.0 is shown in Figure 12. There are differences between the SIMLAR input data and that of the 2-D Lagrangian model. In SIMLAR, the initiation of movement is based on the input of the flow hydrograph at the inflow point which acts as the upstream boundary. The terrain regular grid points are used as the calculation domain of debris flow. Propagation of debris volume is visually visible due to changes in depth obtained from the solution at grid points over the entire terrain. It can be seen that at time 4 s, the downstream tip of the simulation results of both methods reach nearly the same location. However, the results of the Lagrangian method reach a longer distance (less than ten meters).
SIMLAR test for bed slope of 1.0 is shown in Figure 12. There are differences between the SIMLAR input data and that of the 2-D Lagrangian model. In SIMLAR, the initiation of movement is based on the input of the flow hydrograph at the inflow point which acts as the upstream boundary. The terrain regular grid points are used as the calculation domain of debris flow. Propagation of debris volume is visually visible due to changes in depth obtained from the solution at grid points over the entire terrain. It can be seen that at time 4 s, the downstream tip of the simulation results of both methods reach nearly the same location. However, the results of the Lagrangian method reach a longer distance (less than ten meters).
Figure 14. Long-section for Lagrangian model run test 02S1.
Figure 14. Long-section for Lagrangian model run test 02S1.
Figure 13. Lagrangian model run test results on uniform bed slope (tan 6,, = 1.0) with bank slope (tan 6, = 1.0). (a) at initial condition, (b) at t = 2s, (c) at t = 3s, (d) at t= 4s.
Figure 13. Lagrangian model run test results on uniform bed slope (tan 6,, = 1.0) with bank slope (tan 6, = 1.0). (a) at initial condition, (b) at t = 2s, (c) at t = 3s, (d) at t= 4s.

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