1:45 PM - 3:15 PM
[O11-P113] The simulation of lava flows in Izu Oshima Island with consideration of temperature, viscosity, and friction
Keywords:The simulation of lava flows, Izu Oshima Island
I Purpose and background
We visited Izu Oshima Island on February of 2025, and we learned about volcanic activities on the island there. Izu Oshima has been erupting regularly at the pace of 36-38 years since Anei Eruption in 1777, and 39 years have passed since the last eruption in 1986, so we can predict that the volcano can erupt very soon.
During the eruption in 1986, lava flow reached very close to the central city of the island, Motomachi, and all people living on the island were forced to evacuate by ships. If Mt. Mihara, the volcano on Izu Oshima Island, erupted again, we should predict the speed of lava flow and the time it will take to reach cities, so that we can consider proper correspondence such as evacuation.
However, complicated simulations can take a whole day to complete calculations, and they might not be useful enough in case of emergency. On the other hand, experiments using 3D models and liquids similar to lava can be done quickly and easily, but we might get wrong results depending on the way we pour those liquids. So, we decided to develop a mathematical simulation that is both efficient and accurate. We will also consider how they can be useful in emergency situations.
II Researching method
We will consider these forces below as things that work on lava flow.
I Divided forces of gravity horizontal to the slope
II Friction with the ground
III Shear stress
We will consider the tip of lava flow as one object, for simplification. The way forces work on lava flow is described in figure 1.
Three forces above can be described as (1) (Equations are shown in the picture)
III will be described as above because lava can be defined as Bingham fluid.
The acceleration of lava flow will be described as (2)
Therefore, the speed of lava flow t seconds after eruption will be described as (3)
viscosity coefficient will be described as (4)
temperature t seconds after eruption will be described as (5)
Velocity gradient will be described as (6), so speed will be described as (7)
By assuming equilibrium velocity for simplification (8)
By adding the effect of initial velocity (9)
The traveling range of lava flow t seconds after eruption will be described with integration as (9)
We will use this equation for our simulation.
III Result
First, we will match our simulation result and past eruption records to consider the validity of this equation. The way we use this equation is described as follows: Input the length of the specific area into X (the length needs to be the length of the slope) Calculate the average gradient of the area Input the approximated triangular numbers of the gradient into theta The simulation of 1986 eruption from fissure crater C using graph calculating soft Desmos is shown in figure 2.
We determined each parameter in the equation as (10), referring to actual data. Each of them is set in a reasonable range of basaltic lava.
As a result, we predicted the arrival time of lava flow 13 minutes earlier than actual data. It shows that This simulation predicts a worse situation, so we believe this can be useful from the perspective of disaster prevention. Also, we think this difference was caused because we didn’t input the effect of trees, rocks, water, and any other prevention inside the equation.
It took around 10 minutes to input the length and average gradient of the area and complete the calculation on Desmos. This indicates that this simulation is also useful in case of emergency.
Simulation of Ura Desert area is shown in figure 3. This area is where the lava flow is predicted to go if there was a big eruption from the main crater, in the experiment using 3D model. In this simulation, it took 63 minutes to flow 3.7 km.
IV Conclusion
Precise lava flow simulation takes a lot of time to complete the calculation and isn’t suitable in case of emergency, but we found out that simplified simulation can also predict approximated flow of lava in short time. This simulation doesn’t consider some frictions and other matters, but it is suitable for disaster prediction because it predicts worse situations. From now on, we want to add another dimension to our graph so that we can simulate the area, not just the distance. Also, we want to consider whether we can use the same equation to predict pyroclastic flow as well.
(Special thanks)
Izu Oshima Geopark Ms. Tanaka Yurika
Asia Air Survey CO.LTD
We visited Izu Oshima Island on February of 2025, and we learned about volcanic activities on the island there. Izu Oshima has been erupting regularly at the pace of 36-38 years since Anei Eruption in 1777, and 39 years have passed since the last eruption in 1986, so we can predict that the volcano can erupt very soon.
During the eruption in 1986, lava flow reached very close to the central city of the island, Motomachi, and all people living on the island were forced to evacuate by ships. If Mt. Mihara, the volcano on Izu Oshima Island, erupted again, we should predict the speed of lava flow and the time it will take to reach cities, so that we can consider proper correspondence such as evacuation.
However, complicated simulations can take a whole day to complete calculations, and they might not be useful enough in case of emergency. On the other hand, experiments using 3D models and liquids similar to lava can be done quickly and easily, but we might get wrong results depending on the way we pour those liquids. So, we decided to develop a mathematical simulation that is both efficient and accurate. We will also consider how they can be useful in emergency situations.
II Researching method
We will consider these forces below as things that work on lava flow.
I Divided forces of gravity horizontal to the slope
II Friction with the ground
III Shear stress
We will consider the tip of lava flow as one object, for simplification. The way forces work on lava flow is described in figure 1.
Three forces above can be described as (1) (Equations are shown in the picture)
III will be described as above because lava can be defined as Bingham fluid.
The acceleration of lava flow will be described as (2)
Therefore, the speed of lava flow t seconds after eruption will be described as (3)
viscosity coefficient will be described as (4)
temperature t seconds after eruption will be described as (5)
Velocity gradient will be described as (6), so speed will be described as (7)
By assuming equilibrium velocity for simplification (8)
By adding the effect of initial velocity (9)
The traveling range of lava flow t seconds after eruption will be described with integration as (9)
We will use this equation for our simulation.
III Result
First, we will match our simulation result and past eruption records to consider the validity of this equation. The way we use this equation is described as follows: Input the length of the specific area into X (the length needs to be the length of the slope) Calculate the average gradient of the area Input the approximated triangular numbers of the gradient into theta The simulation of 1986 eruption from fissure crater C using graph calculating soft Desmos is shown in figure 2.
We determined each parameter in the equation as (10), referring to actual data. Each of them is set in a reasonable range of basaltic lava.
As a result, we predicted the arrival time of lava flow 13 minutes earlier than actual data. It shows that This simulation predicts a worse situation, so we believe this can be useful from the perspective of disaster prevention. Also, we think this difference was caused because we didn’t input the effect of trees, rocks, water, and any other prevention inside the equation.
It took around 10 minutes to input the length and average gradient of the area and complete the calculation on Desmos. This indicates that this simulation is also useful in case of emergency.
Simulation of Ura Desert area is shown in figure 3. This area is where the lava flow is predicted to go if there was a big eruption from the main crater, in the experiment using 3D model. In this simulation, it took 63 minutes to flow 3.7 km.
IV Conclusion
Precise lava flow simulation takes a lot of time to complete the calculation and isn’t suitable in case of emergency, but we found out that simplified simulation can also predict approximated flow of lava in short time. This simulation doesn’t consider some frictions and other matters, but it is suitable for disaster prediction because it predicts worse situations. From now on, we want to add another dimension to our graph so that we can simulate the area, not just the distance. Also, we want to consider whether we can use the same equation to predict pyroclastic flow as well.
(Special thanks)
Izu Oshima Geopark Ms. Tanaka Yurika
Asia Air Survey CO.LTD