**ALE**

LS-DYNA ALE (Arbitrary Lagrange-Eulerian Method), coupled with its embedded fluid-structure interaction, aims to solve a series of transient engineering problems characterized by large momentum and energy transfer between Lagrange structures and ALE fluids.

LS-DYNA ALE multi-material formulation solves multiple species of fluids in one ALE mesh. Its versatile fluid-structure interaction algorithm is used to study the interactions between structures and those individual fluids. The multi-material capability, together with its embedded coupling to structures, has been utilized by users from various engineering application areas.

LS-DYNA ALE/FSI package excels in simulating engineering problems in which fluids carrying large momentum or high energy density impact, penetrates Lagrange structures. For examples, explosions, tank sloshing, container dropping, bird strike, projectile-hitting-target, aircraft water landing, tire hydo-planing, etc.

The newly developed ALE essential boundary feature greatly reduced the simulation time by eliminating the needs for fluid-structure interactions between rigid structures and fluids. We expect it is going to be explored by users in packaging, petroleum, chemical, manufacturing industries to study problems like pipe-flow, resin molding.

**Flexible ALE Mesh Motion**ALE mesh employs a moving mesh. Neither does it simply follow the material motion as the Lagrangian mesh nor does it fixes in space as the Eulerian mesh. Rather its motion can be tailored to fit the needs of each individual engineering problem at hand. This flexibility in mesh motion makes it quite computing power efficient with much less elements usage. For examples, prior to the impact the ALE mesh could simply follow the projectile in case one is modeling projectile hitting and penetrating armors; ALE mesh expands in space after the detonation of high explosives, etc.

**Compatible ALE Solver**LS-DYNA ALE method utilizes operator splitting scheme to deal with diffusive and advective terms, respectively. In one time-step, an ALE element would undergo a normal Lagrangian time-step in which momentum equation is solved to update accelerations, velocities and displacements, and an advection time-step in which masses, velocities and element history variables are mapped to the updated mesh.

As the ALE Lagrange time-step solution process is exactly the same as the one of the normal explicit FEM solver, the ALE solver is naturally compatible with LS-DYNA structure solver. Compared with traditional CFD solvers, LS-DYNA ALE solves for less equations and could direct utilizes LS-DYNA material library.

**ALE Multi-material Capability**LS-DYNA ALE uses interface construction method to reconstruct fluid interfaces between multiple fluid after the advection process. This technique allows the modeling of multiple materials in one ALE mesh. For example, we could define different material group such as gasoline, vapor inside and air outside when simulating tank sloshing, in one ALE mesh. This way we could not only model gasoline impacting the tank, but also the air outside buckling the tank due to cavitation inside the tank. Take another example, when studying near-field explosions, we could have HE, soil and air defined and consider the impact between soil, HE and structure in addition to air blast hitting the structure while the traditional CONWEP only takes account for the latter. In contrast to other interface tracking schemes such as LevelSet, the interface construction in LS-DYNA ALE doesn"t require solving additional equations. Neither does it need to store extra history variables except element volume fractions.

**Tightly-coupled ALE FSI**LS-DYNA offers ALE/FSI package to deal with the interaction between fluids and structures. Fluids are modeled with ALE multi-material elements (ELEFORM 11); structures with regular Lagrangian elements. Penalty method is used to apply penalty force between the structure interface represented by a grid of coupling points and the fluid interface that is constructed by the interface reconstruction scheme. ALE/FSI package is dedicated to solve the coupling between Lagrangian solids and ALE fluids. Compared with other loosely coupled methods, the information exchange between the ALE fluids and Lagrangian solids are fast, efficient and transparent to users. Also, no iterations between the two solvers are needed. This makes the algorithm very friendly to parallel computing.

ALE/FSI has successfully solved a series of problems in various engineer fields. These problems share the same characteristic of fluids carrying large momentum or high energy density impacting structures.

This large momentum or high energy density is transferred to structure in a very short time, causing large deformations or structure damages. ALE/FSI excels in dealing with engineering problems characterized by transient, high energy, large momentum, largely deformed structures such as explosions, tank sloshing, projectiles, water landing, etc.

**Cost-Efficient ALE Mapping**Along with the 3D ALE solvers, LS-DYNA has two other ALE codes to solve 1D-spherical and 2D-axisymmetric models. A mapping between these 3 solvers can be applied to take advantage of symmetries and speed up the resolution. The solution can be mapped at different locations and times from 1D to 2D, 1D to 3D, 2D to 2D, 2D to 3D and 3D to 3D. Blast loading a structure is an usual application of this method: the blast wave propagation can be quickly solved by the 1D spherical code before the shock reaches the structure, then the wave is mapped on a 3D ALE mesh to solve the fluid-structure interaction problem.

**ALE Single Material Element to Cure Element Distortion**ALE can effectively cure the element distortion in Lagrange solids. One could either refine the mesh or employ high order elements to defer the mesh distortion, but could not solve it completely. With the help of mesh smoothing technique in ALE single material element formulation, we could smooth the mesh around the distorted mesh hence keep the simulation going forward. ALE single material element (ELEFORM 5) uses less computing power, less storage and can handle large deformations and distortions better compared to other engineering techniques.