Chapter 239 - 146: Running the Simulation (2)

Chapter 239: Chapter 146: Running the Simulation (2)

The Alchemist paused for a moment.

"The approach is clever. Very clever."

Zhang Yuan, listening from the side, was stunned. He never expected his typically rigorous mentor to use the word "clever" to describe a method that was, in the world of physics, practically heretical.

But the Alchemist wasn’t finished speaking.

He changed his tone, raising an extremely technical and fatal question.

"But."

The Alchemist tapped his fingers on the tabletop, making a soft TAP-TAP sound.

"When air is violently compressed in a tunnel, it generates immense internal friction and heat dissipation. You’ve packaged this process into a black box, skipping the time derivative."

The Alchemist stared at Chen Zhuo.

"How do you guarantee that the energy at the black box’s entrance and the energy at its exit are, on a macroscopic level, conserved?"

It was a question that hit the nail right on the head.

"Mathematically, if your boundary conditions have even the slightest gap that fails to converge, after hundreds or thousands of matrix iterations, the error will diverge explosively."

The Alchemist’s tone grew serious.

"After a hundred calculations, the error could exceed five percent. If you use that kind of data to build a high-speed rail, it will derail. This set of matrices, without a mechanism to lock down the error, is just a piece of scrap paper."

Zhang Yuan nodded repeatedly from the side.

His mentor had voiced his deepest concern. This was why he was unwilling to just fudge the process with pure algebra; once you lose the constraints of the process, the results are often ridiculously wrong.

Everyone’s eyes once again focused on Chen Zhuo.

They were all waiting for his answer.

Chen Zhuo sat there, looking at the Alchemist, then at the disapproving face of Zhang Yuan beside him.

Chen Zhuo stood up.

He pushed his chair back, leaving the secluded corner.

Under the gazes of the entire research group, Chen Zhuo started walking along the long conference table, heading toward the lectern at the front of the room.

Chen Zhuo walked up to the blackboard.

The wide blackboard was covered with the fruits of Zhang Yuan’s painstaking labor over the past few days.

The complex partial differential equations, boundary conditions, and grid-discretization parameters were densely packed together, like a vast and unsolvable web.

Chen Zhuo lowered his head.

On the floor by the lectern lay the half-piece of white chalk that Zhang Yuan had just dropped.

Chen Zhuo bent down and picked up the piece of chalk.

It was a bit dusty. He rolled it between his fingers, brushing the dust off.

Then, Chen Zhuo turned to face the blackboard.

"Senior."

Chen Zhuo looked at the writing covering the board, then glanced back at Zhang Yuan behind him.

His tone was gentle, with a hint of casual teasing.

"You’ve really filled up the board."

Zhang Yuan stood frozen, his mouth agape. For a moment, he didn’t know what to say. ’At a time like this, this kid still has the nerve to joke around?’

Chen Zhuo turned back, his gaze falling on a partial differential equation on the far left of the board.

It was the source of it all, the cause of every computer crash, the thing that had driven the entire research group to despair: the Navier-Stokes equation, with its time-continuous term.

Chen Zhuo raised his hand and, with the chalk, drew a heavy circle around the equation’s time derivative term.

Then, starting from the circle, he drew a long arrow leading to a relatively clean, empty space in the bottom-right corner of the board.

The chalk touched the blackboard.

The crisp sound of chalk on slate echoed through the dead-silent conference room, without the slightest hesitation or falter.

Chen Zhuo began to speak as he wrote.

"Dean Fang, you’re right. If we ignore the internal friction and heat dissipation, the error will indeed diverge."

Chen Zhuo wrote the beginning of a matrix.

It was a standard Jacobian matrix.

"If we were to simply perform a state mapping, then this set of matrices would indeed be scrap paper."

Chen Zhuo’s chalk glided across the blackboard.

"So, we can’t let it diverge. We have to forcibly rein it in."

Zhang Yuan stood a few steps away, his eyes glued to the formula appearing on the board.

When he saw Chen Zhuo add a complex logarithmic term to the end of the Jacobian matrix, his pupils contracted slightly.

"What is that?"

Zhang Yuan couldn’t help but ask.

The chalk in Chen Zhuo’s hand didn’t stop.

"A non-linear compensation term."

Chen Zhuo replied without turning his head.

"I read the wind tunnel test reports for Germany’s ICE trains from a few years ago. When they handled boundary layer separation on irregular tunnel walls, they also didn’t resort to exhaustively enumerating specific fluid disturbances."

Chen Zhuo drew a straight line on the board, connecting the kinetic energy term at the entrance to the potential energy term at the exit.

"I reverse-engineered their wall compensation approach and embedded it into this matrix."

The people in the conference room were somewhat baffled.

Chen Zhuo paid no mind to the silence behind him.

He took the chalk and drew a heavy line beneath the compensation term.

"I didn’t calculate exactly how much energy was lost inside that black box."

Chen Zhuo turned around to face the Alchemist, who was seated at the head of the table. His voice was clear and resolute.

"At the exit, I imposed a hard constraint."

He tapped the blackboard with the chalk, producing two dull thuds.

"I used the train’s initial kinetic energy from the exact moment it entered the tunnel to hard-cap the potential energy and pressure work after it was fully inside."

Chen Zhuo looked into the Alchemist’s eyes.

"During that 0.01-second interval, the air can be as chaotic as it wants. It doesn’t matter how much heat is generated by internal friction. All that matters is that the energy difference between the initial and final states is completely swallowed by this non-linear compensation term."

Chen Zhuo pointed at the formula on the board.

"Then this matrix will not diverge."

The Alchemist, still seated, shifted his gaze from Chen Zhuo’s face to the lines of writing on the blackboard.