Method and system for real-time simulations using convergence stopping criterion

A computer-implemented method for simulating a physical system, the method comprising:

• accessing a mesh size independent tolerance value of a configuration input;
• simulating a characteristic of the physical system based on multiple models of different mesh sizes for modeling the physical system by iterative processes calculating potential solutions, the multiple models including a first model of a first mesh size and a second model of a second mesh size;
• calculating a new potential first solution for a first iterative process based on the first model, the first iterative process having one or more previously calculated potential first solutions;
• calculating a new potential second solution for a second iterative process based on the second model, the second iterative process having one or more previously calculated potential second solutions;
• determining if the new potential first solution satisfies a convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential first solutions and the new potential first solution, wherein the first iterative process stops when the convergence criterion is satisfied by the new potential first solution;
• determining if the new potential second solution satisfies the convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential second solutions and the new potential second solution, wherein the second iterative process is stopped when the convergence criterion is satisfied by the new potential second solution;
• and
• generating an output to indicate the simulated characteristic of the physical system in response to the new potential first solution and the new potential second solution satisfying the convergence criterion based on the mesh size independent tolerance value.

A system, comprising:

• a network interface for connecting to a network;
• a memory storing instructions;
• one or more processors coupled to the network interface and the memory, the one or more processors executing the instructions from the memory, the instructions including:
• accessing a mesh size independent tolerance value of a configuration input;
• simulating a characteristic of the physical system based on multiple models of different mesh sizes for modeling the physical system by iterative processes calculating potential solutions, the multiple models including a first model of a first mesh size and a second model of a second mesh size;
• calculating a new potential first solution for a first iterative process based on the first model, the first iterative process having one or more previously calculated potential first solutions;
• calculating a new potential second solution for a second iterative process based on the second model, the second iterative process having one or more previously calculated potential second solutions;
• determining if the new potential first solution satisfies a convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential first solutions and the new potential first solution, wherein the first iterative process stops when the convergence criterion is satisfied by the new potential first solution;
• determining if the new potential second solution satisfies the convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential second solutions and the new potential second solution, wherein the second iterative process is stopped when the convergence criterion is satisfied by the new potential second solution;
• and
• generating an output to indicate the simulated characteristic of the physical system in response to the new potential first solution and the new potential second solution satisfying the convergence criterion based on the mesh size independent tolerance value.

A non-transitory computer-readable medium storing instructions for commanding

• one or more processors to perform a method, the method comprising:
• accessing a mesh size independent tolerance value of a configuration input;
• simulating a characteristic of the physical system based on multiple models of different mesh sizes for modeling the physical system by iterative processes calculating potential solutions, the multiple models including a first model of a first mesh size and a second model of a second mesh size;
• calculating a new potential first solution for a first iterative process based on the first model, the first iterative process having one or more previously calculated potential first solutions;
• calculating a new potential second solution for a second iterative process based on the second model, the second iterative process having one or more previously calculated potential second solutions;
• determining if the new potential first solution satisfies a convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential first solutions and the new potential first solution, wherein the first iterative process stops when the convergence criterion is satisfied by the new potential first solution;
• determining if the new potential second solution satisfies the convergence criterion based on a comparison between the mesh size independent tolerance value and a combination of a sum of absolute values and a sum of absolute differences between consecutive iterations of the one or more previously calculated potential second solutions and the new potential second solution, wherein the second iterative process is stopped when the convergence criterion is satisfied by the new potential second solution;
• and
• generating an output to indicate the simulated characteristic of the physical system in response to the new potential first solution and the new potential second solution satisfying the convergence criterion based on the mesh size independent tolerance value.