A new dynamic subgrid-scale model for turbulence is introduced, where the error in the Germano identity is minimized along fluid paths rather than over statistically homogeneous directions. This approach allows the model to be applied to complex flows without homogeneous directions. The model uses a Lagrangian time scale for averaging, ensuring numerical stability when combined with the Smagorinsky model. It is tested successfully in forced and decaying isotropic turbulence, fully developed and transitional channel flows. In homogeneous flows, results are similar to the volume-averaged dynamic model, while in channel flows, predictions are superior to the plane-averaged model. The relationship between averaged terms and vortical structures is investigated. Computational overhead is kept low (about 10% more than the volume-averaged model) using an approximate scheme for Lagrangian tracking. The dynamic model uses the Germano identity to compute model coefficients by minimizing error along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model's time-scale T is chosen to control the memory length of the Lagrangian averaging. Several choices are possible, with option (f) being particularly attractive as it relates to energy flux. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model is implemented in a LES for forced isotropic turbulence on a 32³ grid. The code is a variant of the pseudo-spectral method. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show theA new dynamic subgrid-scale model for turbulence is introduced, where the error in the Germano identity is minimized along fluid paths rather than over statistically homogeneous directions. This approach allows the model to be applied to complex flows without homogeneous directions. The model uses a Lagrangian time scale for averaging, ensuring numerical stability when combined with the Smagorinsky model. It is tested successfully in forced and decaying isotropic turbulence, fully developed and transitional channel flows. In homogeneous flows, results are similar to the volume-averaged dynamic model, while in channel flows, predictions are superior to the plane-averaged model. The relationship between averaged terms and vortical structures is investigated. Computational overhead is kept low (about 10% more than the volume-averaged model) using an approximate scheme for Lagrangian tracking. The dynamic model uses the Germano identity to compute model coefficients by minimizing error along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model's time-scale T is chosen to control the memory length of the Lagrangian averaging. Several choices are possible, with option (f) being particularly attractive as it relates to energy flux. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the model produces equal or superior results compared to spatially-averaged versions. The model's computational cost increases by about 10% compared to spatially-averaged approaches. The model is implemented in a LES for forced isotropic turbulence on a 32³ grid. The code is a variant of the pseudo-spectral method. The model coefficient is determined by minimizing the error in the Germano identity along particle trajectories. This leads to relaxation transport equations that carry statistics forward in Lagrangian time. The model is applied to various test cases, including forced and decaying isotropic turbulence, fully developed and transitional channel flows. Results show the